Fermion fields must satisfy anticommutation relation. But why? I know that unless they anti-commute the Pauli exclusion principle cannot be satisfied. But is there some other deeper/fundamental principle (such as locality or something) which dictates that fermions should anti-commute while bosons commute?
You got it in the opposite direction.
You can always argue that there must be two kinds of fields - commuting and anti commuting.
Commuting fields are defined (rather named) as fermionic fields. Similarly for bosonic fields.
Later, through the Spin Statistics Theorem, Pauli showed that anti commuting fields should have half integer spin and commuting fields integer spins.
Thus it's said that fermions have half integer spins, and bosons have integer spins.
Look up my answer in the above link for the details.