So I enter a game and I am met with an 8v6, clearly advantagous. However, my luck in the game was horrible as even after right clicking the target with an 87% hit chance, I missed. This happenned 3 times in a row and I lost in the end as they took out 2 guys in a row every other turn. This was on easy difficulty (I am a beginner). Is there something I'm not doing properly or is it that I just have really bad luck? I was crouching my units at key positions such as behind different kinds of blocks, setting a single designated healer and sweeping the map in teams of 2.

Sounds like bad luck - although I wouldn't sweep in teams of two, I'd generally sweep with the whole team so they can all support each other. That way you can generally get way more shots on a target in a turn, which helps to minimise any bad luck you may have.

That does sound like bad luck. But you can increase your chances with good tactics. Check some of the strategy guides available. and like squid830 said, keep your guys close together to support each other. You will need multiple shots to take out an alien. Use automatic fire to suppress them so they can't return fire. Use fragmentation grenades if they are close enough (but have movement points available in case your soldier drops the grenade at his feet!) If you are near the end of a round and it looks like trouble is coming, lob a smoke grenade to make it harder for them to return fire. I also found the rocket launcher a great tool for destroying the cover the alien is using.

I'm still learning this game too. I just learned a couple of days ago I could right click when shooting to take an "aimed" shot for a higher chance to hit.

If your still having trouble, check out the youtube videos on combat strategy.