Expresses the idea that 'it's not that I don't...'; 'it's not that there aren't...'
Long explanation:
The grammar point Verbないものでもない is used to express the idea that something is not non-existent, or it's not entirely impossible or incorrect. Literally, it can be translated to English as 'it's not that I don't...' or 'it's not that there aren't...'. It is often used to deny the negative form of a verb, expressing that the situation in question may not be absolutely impossible or incorrect.