Difference Between Belief and Valuing
It's a mental conflict many practitioners face every day. I humbly submit how I perceived the cause and effect behind it: 

1) You learn (i.e. intellectually) that Buddhism teaches the self is an illusion. However, you haven't realized (in both senses of the word) this yet.

2) Your self (Western psychology would say your ego) doesn't like this idea. Nor does your id. They perceive it as death. (In Zen for example attaining Buddha-hood is called "Great Death"). "If the self is an illusion, I don't actually matter/exist"

3) Ego and id will manifest more vigorously and alluring as you practice more, fighting against their "impending doom". They will cling to anything that affirms your individuality or negates your knowledge of the illusionary nature of self. To a certain extent, you could even consider it an instinctive survival mechanism.