Microsoft out-sleazed them by exploiting their pride, that’s the reason. IBM was in a huge rush to get SOME Home Computer out before the 80s were over. They had snubbed the very idea of computers in the home and let Apple and Commodore steal a rich market from under their feet.
So they didn’t even bother scrutinising the contract: They didn’t think that the BIOS could ever be cloned, and if it was, they figured they’d just sue any company that did out of business. So Microsoft having their own version of DOS was “no threat”, as without the BIOS, DOS could run on any 8086 processor but that wouldn’t make it work with IBM software.
But the court ultimately sided with Compaq (not Eagle, Eagle got into trouble) as their BIOS clone was a cleanroom reverse-engineering project and therefore “fair use”, and that was curtains for IBM.