1 When the LORD thy God shall bring thee into the land whither thou goest to possess it, and hath cast out many nations before thee, the Hittites, and the Girgashites, and the Amorites, and the Canaanites, and the Perizzites, and the Hivites, and the Jebusites, seven nations greater and mightier than thou;
2 And when the LORD thy God shall deliver them before thee; thou shalt smite them, and utterly destroy them; thou shalt make no covenant with them, nor shew mercy unto them:
3 Neither shalt thou make marriages with them; thy daughter thou shalt not give unto his son, nor his daughter shalt thou take unto thy son.
Here is the passage in context (with just a single verse added):
“When the LORD your God brings you into the land that you are entering to take possession of it, and clears away many nations before you, the Hittites, the Girgashites, the Amorites, the Canaanites, the Perizzites, the Hivites, and the Jebusites, seven nations more numerous and mightier than you, and when the LORD your God gives them over to you, and you defeat them, then you must devote them to complete destruction.
You shall make no covenant with them
and show no mercy to them.
You shall not intermarry with them, giving your daughters to their sons or taking their daughters for your sons,
for they would turn away your sons from following me, to serve other gods. Then the anger of the LORD would be kindled against you, and he would destroy you quickly.
Thus the answer is because God didn't want Israel to serve the gods of the people who were already in the land.
Importance of context
This site is about hermeneutics, which means trying to understand what the text is saying. So, a good rule of thumb is that if the text says:
Do A because of B
Then rather than wondering to yourself "why A?", we read further and see that the answer is "B".
This is why it's a good idea to read the context around a verse, since sometime the narrative is structured as:
Because of B do A
So you may need to read a few verses before and a few verses after to understand a passage in question.
Doing that -- reading the context around a verse, is part of your basic due diligence when trying to understand what any given passage is saying.
It is generally a bad idea to expect other people on this site to do that work for you, but I'm assuming you didn't know to read a little farther before asking the question, so I'm going through all this now to help you know what to do before asking the next question.
After knowing the context
That doesn't mean everything is cut and dry. You can still wonder, "what does B have to do with A"? -- E.g. you can wonder why having two different belief systems side by side might lead to some kind of mixing between them, or you can wonder why God would have a problem with idolatry, etc. Perhaps this is patently obvious, but in case it's not, let's look at the prohibitions:
God didn't want
their culture to coexist with Israelite culture in the same place, hence no covenants were to be signed
any intermarriage to occur, so that the foreign partner would not sway the Israelite partner
any mercy to be shown, so that the Israelites would not allow their feelings of mercy to give clemency to the tribes and thus allowing 1) and 2) to occur, because as long as there were pockets of idolatry, there was a risk of it spreading.
The above is an explanation of the already-detailed reasoning that God gave Israel.
The reason God told the Israelites to do this is actually given in the following verse of Deut 7 -
4 because they will turn your sons away from following Me to serve other gods. Then the anger of the LORD will burn against you, and He will swiftly destroy you.
5 Instead, this is what you are to do to them: tear down their altars, smash their sacred pillars, cut down their Asherah poles [= phalic symbols], and burn their idols in the fire. 6 For you are a people holy to the LORD your God. The LORD your God has chosen you to be a people for His prized possession out of all peoples on the face of the earth.
It appears that God wanted to stamp out these pagan religions - the reason for this was simple - all involved appalling sexual child sacrifice and child abuse, etc. Most also involved temple prostitution and much ritual cutting etc. Such degrade the humanity and freedom of all who thus engage (in a similar effect as modern pornography and violence does.)
The above instruction in Deut 7 was moderated by another requirement as listed in Deut 20 -
10 When you approach a city to fight against it, you are to make an offer of peace. 11 If they accept your offer of peace and open their gates, all the people there will become forced laborers to serve you.
12 But if they refuse to make peace with you and wage war against you, lay siege to that city.
Thus, it appears that all cities were offered a chance to become part of Israel and abandon their pagan violence.
The understandings behind the actions taken by the Israelites during their wilderness experience, and then after they entered the land God had allocated for them has recently received a different viewpoint. And this outline summarises this for your consideration.
Although these are only recently coming into consideration, they are not ‘new’, nor recent. In fact they are sourced earlier than the traditional viewpoints presented by tradition. More attention is being taken of some non canonical literature, such as the book of Enoch (1), and historians from the time of the second temple, for example Josephus.
Previous to ‘recently’ and even still currently, these books and writings were disregarded due to the number of blatant forgeries and intentional heretical works based on ‘so called’ findings - and even today we need to exercise caution when considering these extra sources (outside of the Bible.). This has fuelled the defence of the traditional doctrines of the 15/16th centuries which somewhat conflict with these recent directions.
But there is increasing evidence, archaeological findings, Dead Sea scrolls, and scholarly analysis of the Semitic languages - especially Hebrew.
And overview ... there are 3 significant events that need to be considered when ‘assessing/interpreting’ the actions in the promised land. The first being the Fall, Genesis 3, pretty well accepted as a “root’ cause. But next we have the flood...
GEN 6:4 The Nephilim were on the earth in those days, and also afterward, when the sons of God came in to the daughters of man and they bore children to them.
This is now being seen as an evil attempt to corrupt the genetic line of ‘man’ - so as to prevent the Messiah (corrupt the seed of the women - Gen 3:15). Note that Gen 6:4 tells us that these Nephilim would be present after the flood!
The third event is Babel. Post flood. Nimrod, one ‘world leader’. The result of this one world rebellion against God was God dividing up man into nations.
DEUT32:8 When the Most High gave to the nations their inheritance, when he divided mankind, he fixed the borders of the peoples according to the number of the sons of God.
God allocated land - and set boundaries! And the ‘sons of God’ put over these nations knew the boundaries. And here God allocated Canaan, the ‘promised land’ for himself. Nevertheless some tribes/nations intentionally ‘squatted’ and set themselves up in Canaan. Intentionally to disrupt Gods plan (of redemption.). And they had had 100’s of years to do this, so we’re well fortified. And then there are the Nephilim (Numbers 13), men of great strength, size.
It is these ‘groups’ that the Israelites had to ‘cleanup’. The Amorites, and the Canaanites, and the Perizzites, and the Hivites, and the Jebusites, - all decedents of Canaan, Noah’s ‘son’, who was cursed. These groups were evil, illegal squatters, and corrupted ‘genetically’ (Nephilim). They were intentionally in this land to defy God, but more, to Thwart Gods plan of redemption. They needed to be removed. Else we today would have been un-saveable.
Genesis 15:13-16 13 Then the Lord said to Abram, “Know for certain that your offspring will be sojourners in a land that is not theirs and will be servants there, and they will be afflicted for four hundred years. 14 But I will bring judgment on the nation that they serve, and afterward they shall come out with great possessions. 15 As for you, you shall go to your fathers in peace; you shall be buried in a good old age. 16 And they shall come back here in the fourth generation, for the iniquity of the Amorites is not yet complete.”
Here God implies that at least part of the reason for the delay in the children of Abraham returning to the land of Caanan to possess it is that Caananites just weren't quite sinful enough. From this verse, I see the Judgement against the land of Caanan similar to the judgment of the world of Noah. The people were exceeding bad and God was ready to wipe them out.