Well, there are a couple reasons:
1. The continuity wouldn't make sense at all. Peter lives in New York City, which is attacked by Loki and the Chitauri in the first Avengers movie. It was also attacked by the Abomination in "The Incredible Hulk". Where was Spider-Man during any of this? Unless they went the "all the Spider-Man movies happened before the MCU-storyline even started"-route, it wouldn't make sense. If they DID take that route...then where is Spider-Man when New York needs him the most? They can't have these movies take place AFTER The Avengers either, unless they really wanted to force it down our throats.
2. What role could Spider-Man even have in The Avengers? A lot of his character traits are already seen in Iron Man -- technological genius, wiseass, deals with personal hardships by being a hero, etc. If they found a logical way to fit TASM into the MCU, we'd have a mini-Tony Stark, just with superpowers.
3. While most people would probably like to see a wiseass Spider-Man alongside Robert Downey Jr.'s Iron Man, I find the idea cringeworthy. The two of them spewing sarcastic one-liners the whole movie would get infuriating. The Avengers knew how to balance the humor with the characters they were given because each character had a certain personality that kind of bounced off each other for a comedic effect. As MCU's Iron Man and TASM's Spider-Man have the same sense of humor, it would become redundant.
4. The Avengers is more about the heroes, while TASM is more about Peter trying to BECOME a hero. By the time of The Avengers, most of the main characters had their characterizations and origin stories, while TASM seems to be stretching the becoming of Spider-Man for more than just one movie.
5. Everybody Knows That Peter Parker is Spider-Man? No thanks!
6. Spider-Man -- as well as many of his villains -- are more personal and usually have very complex backgrounds and motivations. While most people may not give TASM a lot of credit for its story, I found it fascinating that the conflict between Spider-Man, Captain Stacy, and the Lizard seemed to be their different ways of carrying out justice. They all found flaws in humanity and attempted to change it in their own way. Spider-Man at first fought for just himself, but soon took responsibility for others even though he was at one point just an ordinary citizen. Stacy used the law to carry out justice. The Lizard saw humanity's flaws as something that needed to be changed by force.
In the Avengers, we have Loki as a villain and the main conflict between him and The Avengers is that he wants to destroy the world while they want to save it. And that's fine, it worked perfectly for the movie, but I think it'd be stupid to just forcibly change the themes we've seen in the first TASM movie in order to fit it into The Avenger's theme of good vs. evil.
So, yeah, I really think Spider-Man should be left out of the Avengers. Like, as a whole, until both franchises reach their ends and new ones begin.