Military suspicious of working with Russians
I think the Pentagon is concerned about sharing US sources and tactics with a potential adversary. It has been roughly 73 years since the US and Russia were on the same side in a war and in that one they were engaged in separate theaters of operation. There is also probably a feeling that the Russians stand to gain more from the cooperation than the US does.
President Trump has said the U.S. should ally with Russia to combat militants in Syria, but Defense Secretary Jim Mattis has said he doesn’t see Russia as trustworthy.