You’re asking a difficult question that’s attracted a lot of commentary and speculation!
Jonathan Pennington addresses many relevant contextual, cultural, and linguistic factors in his excellent ~400-page book, Heaven and Earth in the Gospel of Matthew, which was derived from his PhD thesis on the subject. It’s a thorough academic investigation, but not an easy read.
To answer this question, one needs to understand what Jesus meant by “the kingdom of the heavens,” a new term found only in Matthew (along with “kingdom of God”), understand that it was translated into Greek from the original Aramaic, which complicates things a little, and address many questions and issues.
In the literal Greek in English word order with amplified words), we read
“And from the days of John, of the one immersing, until just now, the
kingdom of the heavens is forced [Strong’s Greek 971: biazó, forced
with violence] and it is snatched/seized by assailants/violent men
[Strong’s Greek 973: biastés, masculine noun].”
Questions to answer:
• What exactly started in the days of John the Baptizer? Did it end with Jesus or is it continuing?
• What exactly did Jesus mean by “the kingdom of the heavens”? The term is found only in Matthew.
• Who exactly are these violent men?
• How are they seizing or snatching the kingdom of the heavens?
A hint comes from Matthew 7:21-23, again in literal Greek except for word order and a couple of interpolated words
“Not everyone who says to me, ‘O Lord, O Lord,’ will enter the kingdom
of the heavens, but only the one who does the will of my Father who is
in the heavens. Many will say to me on that day, ‘O Lord, O Lord, did
we not prophesy in your name, cast out demons, and in your name do
many powerful works?’ Then I will acknowledge to them that at no time
I knew you, retreat from me O ones working lawlessness!’”
Jesus also warned his followers in John 10:1,7,8 NASB
“Truly, truly I say to you, the one who does not enter by the door
into the fold of the sheep, but climbs up some other way, he is a
thief and a robber.”
So Jesus said to them again,
“Truly, truly I say to you, I am the door of the sheep. 8 All those
who came before Me are thieves and robbers, but the sheep did not
listen to them.
My conclusion from my reading and study of the issues is that there were men who were trying to insert themselves into the “Jesus Movement” of that day to try to gain control over it and become its leaders.