insurance company query

[rterry]

i have sustained roof damage during the recent and continuing NYC winter rain a nd snow and ice. the damage has caused leaking in a kitchen area. the ceiling and walls are damaged as well as floor tiles. the insurance company is willing to pay for the internal damage (they want pictures and a detailed analysis from a contractor). however, they seem to be hesitant about incuuring the cost of the roof problem. they seem to be "fineprinting" the policy. words like wear and tear, proper roof maintenace, defect, etc. how do i properly show that this problem was not something that i did but merely circumstances of the weather. the roof is a good condition roof. PLEASE ADVISE if you can