Did you give any reason why he felt it's a lose lose situation? I mean, if there is no issue between you two and when you regularly talk to each other with 'what you two have been up to', it's only natural to mention what he's been up to or/and with whom.
He would feel a lose lose situation if he thinks you overreacted or he actually hangs out with someone inappropriately. If there is complete trust between you two, either of you should feel 'whether he/you should mention this or that'. You two should feel VERY comfortable talking about each other's routines and encounters....
“Really, sex and laughter do go very well together, and I wondered - and I still do - which is more important.” - Hermione Gingold-