Tchaikovsky's last symphony is not exactly a classical symphony in the usual sense of the word "classical". Let us look at its first and most important movement where one expects to hear something that is more or less in sonata form. The exposition contains, of course, two main themes, the second (and most beautiful) of which, however, is totally absent from the development section - and even from the recapitulation! It is only heard as a kind of coda at the end of the movement.
The second movement is in ABA form, the tone of the middle section foretelling the tragic tone of the finale (fourth movement) of the symphony. Finally, the energetic third movement is a standard Scherzo (albeit not in 3/4).
We note that Gustav Mahler has been quite unjust in his criticism for the symphony, calling it "shallow, superficial, distressingly homophonic - no better than salon music"! According to Deryck Cooke, Mahler attempted to "correct" the shortcomings of the "Pathetique" in his own "Ninth", which owes much to Tchaikovsky's "Sixth"...