They agreed to the borders stated by the UN,

That's an oversimplification - the borders imposed by the UN were significantly smaller than the borders that were desired and obtained by Israel in the course of the war, which are those of the Green Line.

But that's not particularly relevant to the issue today, which is whether there are any valid reasons why a Palestinian state should not be recognised as a member of the United Nations.

One reason which has been given in media disussion is that this could mean that Israel would be subject to the scrutiny of the International Criminal Court in relation to its actions, including the establishments of illegal settlements in occupied territory. I cannot see how this can be seen as a valid ground for opposing recognition of Palestine.