Actually, the early popes, bishops, etc. tended to be martyred. It didn't become safe to be a Christian until somewhat later.
Your friend is correct, however, that the property question was one (not the only) consideration touching on celibacy. The church -- not the priest, bishop, or pope -- accumulated great wealth through bequests, and the institutional Church wanted to avoid the temptations of benefices becoming quasi-heriditary.
As I understand it, however, the ideal of celibacy was honored in the western church from a very early period, long before property would have been much of a consideration and certainly before the rule became mandatory. The personal example of Jesus was central to this. The idea current in the early church that the Second Coming was imminent also played an important role.
Perhaps one of our house experts will be good enough to weigh in on this.
Fair enough, although one could argue that celibacy didn't become established until that same "later." :)