The problem is that against bots, the beginner bots seem awfully frail. Being AI, they lack the natural adaption of human players, and in moments of lacking threat analysis or sometimes outright stupidity, they can be easy targets that don't teach a whole lot. The flip side is the intermediate bots, which I could swear are given a subtle artificial advantage in gold gains and health, complete with "cheating computer" reactions and impossible situational awareness and team coordination to offset the usual AI holes. They can range from impossibly difficult steamroller games from mildly challenging.
PvP is where the glaring problems really rise up, though. The game can be played instinctively and adaptively, but you really have to get the right feel for it. More often than not, a 'good' player has done some degree of study on optimum builds, and has memorised solid strategies. Familiarity with the characters is also a fairly big part of the game too, which can take some time. On top of this you have summoner levels, which despite everyone's insistence on it playing only a minor role, can really tip the balance. Being able to have an additional 3% lifesteal or 10% cooldown reduction doesn't sound like much, but it gives you that little edge in the early game, and just sits on top of all your other stat gains towards the end. Then you have the typical PvP playerbase, where everything is everyone else's fault, teammates may randomly decide to idle for 10 minutes in a match or decide they don't want the lane they called, and join yours without saying a word just as the enemy pushes a turret.
LoL is a bit like L4D. It has great potential to be fun and intense, but the disparity between people who play it for fun, and people who play it to win at all costs (including sacrificing fun) is pretty huge. If you play with plenty of friends, the experience gets substantially better, but in the event of a lopsided match, it is easy to end up impossibly frustrated and feeling the long stretch of game-time was just an exercise in futility. My suggestion is to stick to bots. Beginner until you learn the ebb and flow of when to push and when to focus on self-preservation, and then intermediate when you want to step it up. Or alternatively, like L4D VS, you can get sick of the random uphill battle to achieve some fun, and storm off to play something more accessible.