Why don't we see super-symmetric particles?

we can se many particles, also we can detect and produce antimatter

however my question is why even at high energies we can not see any supersymmetric partner of a particle ?

Supersymmetry is not an experimentally verified theory. There are two possibilities:

1 The SUSY scale is significantly higher than many would have argued before LHC or otherwise hidden.
2 SUSY does not exist.

I vote for 2.

Meir Achuz said:

I vote for 2.

If only it was a voting game ...

Vote early and vote often.

There is also the possibility that the spectrum is such that it is just too hard to see. For example, if you had a stop squark just a little heavier than the top quark and only a moderately heavy LSP, you'd produce a few percent extra events that looked like top-antitiop, possibly with a smidgen more missing energy. Hard to spot and very hard to spot if you aren't specifically looking for it,

Vanadium 50 said:

There is also the possibility that the spectrum is such that it is just too hard to see.

I tried to include things like this in 1 with the ”otherwise hidden” to not make it too long …

While there is a whole cottage industry of people who propose hiding places - an industry of which I am not part - having a stop mass near the top mass has some desirable features. Apart from being difficult to disprove. It's not just hard to find.

There is a paper in preparation by one of the LHC experiments that may soon shed some light on this region. Maybe in a month or two it will be in print.