According to Steven Pinker, in The Stuff of Thought: Homonymy usually arises when an ancestral word budded off new senses in a language's history and current speakers retain no inkling of the original connection. For instance, the word odd originally referred to something that stuck out, like the point of a triangle.

Why are there homonyms?

homonyms are the result of mergers and splitters. Borrowings also may be homophonic because they usually are interpreted according to the native phonology, giving rise to slightly more coincidences. Writing systems are woefully incomplete at capturing what a language actually sounds like.

Why do homophones exist in English?

Because the sounds of language change over time and this process doesn't really care whether it causes two previously distinct words to sound the same.