Why exactly did Summer break up with Tom?

In the links to the wiki you gave it tries to explain this in the following paragraphs:

During the next few months Summer and Tom grow closer, despite Summer's telling Tom that she does not believe in true love, and does not want a boyfriend.

Shortly followed by:

On day 290, Summer and Tom end their relationship after they see The Graduate, a film which Tom thinks shows true love

Flipping over to the wiki for the graduate shows that this potentially ties in, though it is hard to take a quote which shows 'true love' I think this bit sums it up best:

With some hesitation, Elaine returns a cry of "Ben!" and rushes toward Benjamin. A brawl breaks out as everyone tries to stop her and Benjamin from leaving. Elaine manages to break free from her mother, who claims "It's too late!", to which Elaine replies, "Not for me!" Benjamin and Elaine escape the chapel by barring the chapel's double doors with a wooden cross, trapping the attendees inside