Hello My website's homepage link has been removed from all google searches with the keyword "hentai" Hentai is defined as adult animation from japan. Think of it as adult cartoon porn. Looks like someone complained that my website has videos of certain hentai series that are licensed and I am violating their copyright. Well that may be true, but still I believe I have the right to counter this dmca because my site is being removed for all searches with keyword "hentai". Hentai is a generic term, it is not owned by any company. It would be like asking google to remove a website from all searches containing the keyword "cartoon" just because this website has videos of The Simpsons. Rather, the dmca should specify the keyword "The Simpsons" and have the said website to be removed from those results. Do I have a cause here to file a counter dmca? I know I'm trying to grasp at loopholes, but please answer constructively.
You are going to struggle, do you actually own the rights to any of the content on your site? If you do then you can file a counter notice giving those URLs explicitly and Google should reinclude those items where you do have the rights, make sure they are on the homepage and non of the offending material is and then you can include the homepage URL in the counter notice. If its all illegal then little option but to accept you've been caught and think yourself lucky its only been a blackballing on Google.
They are not removing the site for certain keywords, they are removing it entirely because it contains copyrighted material. You should be more worried about removing the copyright infringing content rather than trying to counter the DMCA. You are asking for a lawsuit by keeping it up.