What is the argument for this clause again?
I'll try to list the arguments for and against that I've seen. I'm going to try to do this as neutrally as possible and keep my opinion out of this list. I may miss a few arguments for both sides since I'm going off memory here.
For Species Clause
-Let's people spam the same Pokemon to eventually overrun the opposing team. Basically as BK said above. You have a Pokemon that can check and remove Ytwo without much risk to itself. So you KO the opposing Ytwo. Another shows up. You KO that one and are now pretty worn down. Another shows up. Your check is too weak to handle it and you have no remaining checks, so the remaining four Ytwos sweep your team. (Or in other words, bad for the same reason why running, say, 6 Aegislash or 6 Talonflames in OU would be bad.)
-Makes team building less interesting. Aka, why run multiple species of Pokemon when you can just grab the one with the strongest stat you like and spam it? Removing that ability would force players to think more about their team choices.
-Lack of the clause is unhealthy for the meta-game.
-Lack of the clause is unfair to certain playstyles. HO claims it's unfair because double Eviolite Chansey and similar. Stall claims its unfair because multiple XYtwo/Lati@s/Kyu-both/etc.
-It glitches battles. PS is programmed to assume you can only have one of each species. Hence if you send out only Ytwos, only two of them will appear on the display for the opposing team, denying the other player information they would otherwise have. (Do they have two Ytwos or more?)
-It'd give some other Pokemon more of a chance to be used. Aka, right now if you need two Fighting types, you use two Xtwos since they outclass everything else. With species clause, you'd have to take something else, like Heracross or Keldeo.
Against Species Clause
-It's too limiting for the tier.
-It wouldn't really do anything to the tier since most people don't use multiples of the same mon, so why bother implementing it? I've not seen this one mentioned this time
yet, but every previous time species clause was discussed, this argument came up.
-It's unfair to certain pokemon. Basically, you'd have to pick between Xtwo and Ytwo, Kyu-B and Kyu-W, Darm and Darm-Z, Aegis-S and Aegis-B, and certain mons with viable post-megavolution abilities.
-It hurts certain gimmicks, like double Imposter, Sturdinja + Scrapinja, etc.