How to fight insurance claim denial?

[Jerry Poon]

A storm a month ago or so knocked half a tree down. The tree fell right next to a rental and the force took down an entire wall. The damage is about $15k.

I contacted our insurance and they are denying our claim, citing the following:
collapse, including any of the following conditions of property or any part of the property: (1) An abrupt falling down or caving in; (2) Loss of structural integrity, including separation of parts of the property or property in danger of falling down or caving in; or (3)Any cracking, bulging, sagging, bending, leaning, settling, shrinkage or expansion as such condition relates to (1) or (2) above

Their reasoning is that the tree didn't fall directly on the wall itself, and claim that the basement was faulty prior to the incident. We do not have pictures because the demo contractor was removing the tree at the dead of night in the storm.

How do I fight this? It is enraging that in a time of need the insurance company will do what they can do wiggle out of this. Why do I even pay them for the policy?

An attorney I am working with wants to write a letter to try and convince the insurance company on the basis of Efficient Proximate Cause. The attorney's fees for this are about $1k. I had my insurance agent reach out to the adjuster and he seems pretty dug in on his position. Is this letter worth the money to try and argue my case? I am worried that the insurance will just drag this out, demanding more $1k letters, possibly engineering studies, etc.

Any suggestions on what I should do?