There is absolutely no reason why people can't have multiple accounts and try to level up a new account and get high in rank.
Sure, it sucks when you have one against you but they could have also been very much on your team.
I have 2 accounts...my main and then a level like 12 that I'm slowly leveling up and going to rank once I get more champions and runes on it. If I feel I'm playing against a completely new player, I will generally ignore them in lane and just farm...only harassing them or all-ins if they do it first. I won't take free damage but won't kill them just because I have the knowledge to outplay them. Yes some don't care and will just take advantage but you'll get that in any game.
Also I would stop playing if League required a SSN. Being secure or not, I don't trust hackers not to hack in to steal identities. Would be way too easy. Nothing on the Internet is safe and 100% secure.