The key word is trust. If my partner and I are having issues in our relationship related to trust and negative behaviors, probably not the best idea to climb with the opposite sex. Accusing your partner of wanting to sleep with anyone he/she climbs with while you are seeking out members of the opposite sex to go solo with for the day and giving your SO vague information could be argued to be intentionally utilizing triangulation and other control tactics for emotional control and manipulation.
There are definitely appropriate and healthy ways to climb with the opposite sex. Communication, respect and honesty are key.