I’m trying to understand…

Where and how Jesus rules the Old Testament and laws of the covenant obsolete.

A lot of the apologetics argue that Jesus “fulfils” the laws so they are no longer necessary:

From Matthew:

5:16 Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven.
5:17 Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil.
5:18 For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.
5:19 Whosoever therefore shall break one of these least commandments, and shall teach men so, he shall be called the least in the kingdom of heaven: but whosoever shall do and teach them, the same shall be called great in the kingdom of heaven.
5:20 For I say unto you, That except your righteousness shall exceed the righteousness of the scribes and Pharisees, ye shall in no case enter into the kingdom of heaven.

But this directly contradicts many of the assertions of the Old Testament that the laws were eternal and perfect (and thus wouldn’t need to be changed or abandoned):

Psalms 19:7
The law of the LORD is perfect, converting the soul: the testimony of the LORD is sure, making wise the simple.

Psalms 119:160
Thy word is true from the beginning: and every one of thy righteous judgments(laws) endureth for ever.

And furthermore:

Psalms 119:1-4
Blessed are the undefiled in the way, who walk in the law of the LORD.
Blessed are they that keep his testimonies, and that seek him with the whole heart.
They also do no iniquity: they walk in his ways.
Thou(God) hast commanded us to keep thy precepts diligently.

Furthermore, it’s pretty clear that in the Old Laws God did not want people eating certain foods (they were unclean), but Jesus saw fit to not ‘fulfil’ those laws, but was more willing to just ignore them and taught his disciples as such:

Lev 11:42-44
Whatsoever goeth upon the belly, and whatsoever goeth upon all four, or whatsoever hath more feet among all creeping things that creep upon the earth, them ye shall not eat; for they are an abomination.
Ye shall not make yourselves abominable with any creeping thing that creepeth, neither shall ye make yourselves unclean with them, that ye should be defiled thereby.
For I am the LORD your God: ye shall therefore sanctify yourselves, and ye shall be holy; for I am holy: neither shall ye defile yourselves with any manner of creeping thing that creepeth upon the earth.

Mark 7:18-19
And he saith unto them, Are ye so without understanding also? Do ye not perceive, that whatsoever thing from without entereth into the man, it cannot defile him;
Because it entereth not into his heart, but into the belly, and goeth out into the draught, purging all meats?

There’s also  several points when Jesus pisses off the Jews by failing to observe the Sabbath, but it’s very clear in Genesis, Exodus, Leviticus etc. that one who doesn’t observe the Sabbath is to be put to one of a couple serious punishments (since the Old Testament specifies several) – in this law Jesus didn’t really fulfil it, but merely decided to ignore it.

So I pose the question, because I’m not a Theologian, or even a decent expert in the Bible, where am I wrong, and where does it explicitly say that Jesus cancelled the Old Laws?