Poor Tevye. He's a woodcutter then a dairyman; he's got seven daughters, then five daughters, and then—when Chava comes back—he's got six again; he's got a home and a family—and then he's got nothing. No wonder it's so hard to get a read on him. Is he just a modern day version of Job? Or is he defined by being a Jew under an oppressive regime? Or is he defined by his struggle between modernity and tradition in the setting of his family? Tevye never answers directly—unless of course we assume that the answer is (d) All of the above.
Tevye is a fundamentally misogynist book, because women in the story are basically interchangeable placeholders.
Rather than undergoing realistic, human, motivated change, Tevye is an unstable character whose opinions and thoughts vary wildly depending on the needs of the plot. He has no definable personality, and just reads a random collection of opposite attitudes.