But Michael FORCED one of them to play their hand. Tessio was even honest enough to say he would fall under Barzini sooner or later. In front of the don!! Michael was being unreasonable and patronizing to both caporegimes who were unstandably upset and desperate. Clemenza is lucky that Barzini approached the smarter of the two, but Tessio knew he couldn't resist Barzini once he 'made him an offer he couldn't refuse'

This was probably Mike's desire to get rid of a capo, in order to install Rocco's secret regime.