Lag can really affect a match if it occurs at the right/wrong time. Sometimes it's really useful, othertimes it can lead to taking a stock in a BS manner. And that's probably why people hate it so much. It disrupts the game in a way that can make someone who has COMPLETE control of a match suddenly lose.
An example of this...
I'm on the edge with Sonic waiting for an enemy to respawn, let's say I'm at 20%, pretty low. My opponent is right next to me and I want a quick move that will knock them back. I opt for down tilt because it's very fast, has decent range, can also trip the opponent, and I sometimes end up forward smashing when going for a forward tilt, so it's safer for me. Meanwhile, the enemy wants to keep me on the edge, so they opt to jab. Let's say they jab before I DTilt and there is input lag. The jab knocks me off the edge while I'm inputting DTilt while I'm on the ground, I get nudged off the edge and my DTilt now becomes a Dair due to lag, so I plummet downwards. The lag continues and I'm unable to jump or do an UpB before it's too late. I lose a stock and a MASSIVE lead.
It's things like this that would really annoy me personally, and likewise many other people. It takes the wind out of your sails and ruins the match for you. Being on the other end of the spectrum, you shouldn't feel accomplished or good about the SD that's just happened. So nobody really wins.
Now, if you're on about using it to your advantage, there's what I've just said, and then there is abusing it to get out of situations where you'd usually get punished. There have been a few times where I have managed to get out of something I shouldn't have because of a little blip in an online game, where the game slowed down briefly enough for me to escape, and sometimes punish the opponent. The problem is, it's hard to predict lag, there is no telltale sign as to when it'll happen and how bad it will be. That's why it's hard to 100% master it, it's an untamable beast, and we just have to get lucky when lag strikes.