Abolishing the Law would, in the mind of the Jews at the time, be a significant insult--the written Law was what (in the eyes of many) defined their people. They were God's people because He had made a covenant with them. Was that covenant to be abolished? No, it was to be fulfilled.

Abolish

"To abolish" carries a more negative connotation than to fulfil--if something is abolished, this suggests there was something wrong with it, it was in error. Consider the following synonyms of abolish:

abate, abrogate, annul, avoid, cancel, disannul, dissolve, invalidate, negate, null, nullify, quash, repeal, rescind, roll back, strike down, vacate, void (see here)

That's a pretty harsh list.

Fulfil

"To fulfil", on the other hand, suggests that what was given was appropriate for the time and now it has run its course. When something is fulfilled its validity is acknowledged. I believe that this is what Jesus had in mind--He was not saying that Moses was wrong, He was saying that the end purpose of the Law was to point people to Someone (Himself)--who had now arrived--who would fulfil the promises God made with Israel.

This meant He was claiming an authority greater than Moses--an incredible claim that many at the time found difficult to accept.

The Lord wasn't repenting for giving the Law, He was fulfilling its promises

The Epistle to the Hebrews is at its core an extensive argument that the ordinances of the Law were symbols of Christ, and that the old covenant had been replaced with a new covenant.

My (surprisingly off-putting =) ) argument from Hebrews--for Jesus fulfilling the Law by making Himself the ultimate offering--is found here.

Let's look at just 2 passages:

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From Galatians 3, that God gave the Law, but it wasn't an end in itself--it was to point people to Christ:

19 Wherefore then serveth the law? It was added because of transgressions, till the seed should come to whom the promise was made; and it was ordained by angels in the hand of a mediator.

...

21 Is the law then against the promises of God? God forbid: for if there had been a law given which could have given life, verily righteousness should have been by the law.

...

24 Wherefore the law was our schoolmaster to bring us unto Christ

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From Hebrews 7, contrasting the daily ordinances of the Levitical priests with the eternal efficacy of the atonement of Christ:

25 Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.

...

27 Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people’s: for this he did once, when he offered up himself.

The Law of Moses vs. laws in general

It is important to clarify what I'm not saying--I'm not saying the fulfilment of the Law of Moses means there are no more rules or commandments. Jesus fulfilled the Law; He also gave many commandments; this is what the next 28 verses following the passage in the OP are all about.

In what sense did Jesus fulfil the Law?

God made a covenant with Israel; God kept His covenant with Israel.