explain why many anti-christians like to attack God they claim does not exist?
Unless you're referring to physical attacks such as desecrating altars, of course that would be impossible. No one can 'attack' the non-existent.
Although believers may easily confuse an argument that disputes the stated 'logic' of their faith as an attack on their god. Often they may be justified; it's difficult to be concise about the mysterious and ineffable, and many fail.
But I think there's even less justification for asserting what "anti-christians like to attack" than there is for making blanket, prejudiced statements about believers, as if they were all alike.
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PS: As a side-note: Anti-christian refers to Christianity only, and so deserves a capital 'C'. And the most numerous anti-Christians are those who believe in other gods, or in the same God (Muslims and Jews) but deny the divinity of Christ. I took your purpose to be a question about atheists, who believe in no gods at all. Non-Christian believers may phrase their feelings about Christian beliefs very differently.
But, like the atheists, I'd bet they would say they weren't attacking anything that existed.