How about infallible Pope, can he tell the date of the second coming because he is infallible?
But that of course is the problem, you use your own definition of infallibility, not the RCC one, then use it to attack RCC
It is called a straw man argument, it is also a logical falacy.
EVERY Christian believes in infallibility in its proper context, they must do to be Christians, or to believe that scripture is inspired.
That some people can act inerrantly in doctrinal matters, that is God acting through people, which is for example the only way scripture can be inerrant and inspired, for the act of authorship of scripture to be infallible, free from error.
It is a mark of an act under inspiration not of a person, and it does not make that person sin free or inerrant in any other way.
So the only question is who has acted or acts infallibly, not whether infallibility exists.
The pope is only deemed infallible in limited matters of statement ofdoctrine which rarely has happened in 2 millenia. He also presides over councils, that for example declared the canon of scripture, so YOU rely on the authority of those catholic councils to believe that the New Testament is inspired. A simple thank you to the pope and councils will do.
But then the pope has scriptural authority to do so having been given the " keys of the kingdom" an unquestionable reference back to the authority of steward in a davidic kingdom, " what you bind on earth is bound in heaven"