Balrog and The One Ring

[Zigûr]

I'm not sure "he had only a share" means share of the rulership, but rather share in the creation of, hence this statement:

Melkor could do nothing with Arda, which was not from his own mind and was interwoven with the work and thoughts of others

He was not solely responsible for the creation of or nature of Arda; he was only one contributor among many. Thus he came to hate Arda and resent its existence because he believed only his own mind, work and thoughts to be worthy.

That's how it seems to me, at least.

To be fair, I think the passage is saying that Morgoth began with the desire for power over Arda, and that the transformation of that desire into a desire to destroy it came later, as a result of his ever-increasing pride.