"I don't want to attend mass celebrated by those not in full communion. Why should I?"That's a fair question. The answer to it is because unlike you,
some Catholics are superficial people. They would rather attend a "traditional-
looking" liturgy celebrated by schismatics than a
Catholic Mass celebrated by bona-fide
Catholic priests who within and thus are
part of The Church.
"You see question is who is not in full communion this days,who is in the church?"That's an easy matter to clarify.
The SSPX isn't. In his Apostolic Letter
"Ecclesia Dei" Pope John Paul II confirmed the excommunication of Abp. Lefebvre and while doing so wrote that
"formal adherence to the schism is a grave offence against God and carries the penalty of excommunication decreed by the Church's law."In a word, the SSPX's clergy are NOT in The Church and neither are those in the laity who formally adhere to the SSPX's schismatic ideology.
It is a basic matter of Catholic principle, self-explanatory really, that The Pope is the temporal
head of The Church, so he is irrefutably -IN- The Church by virtue of being
head of it. Pope John Paul II confirmed the excommunication both of the SSPX's founder and made special mention that it also applies to anyone who "foramlly adheres" to the SSPX's schism.
See how easy that was? Glad I could help.
:) 
