Your problem is not with Catholic teaching, It is with Protestant teaching. Protestant teaching says that we continue to re sacrifice Jesus over and over. Catholic teaching says we offer the SAME sacrifice as Jesus on Calvary in an un bloody manner and Jesus asks us to do this often. As you do, I too have a problem with the re sacrifice of Jesus over and over and you are correct Protestants should give up this teaching. A misrepresentation of Catholic teaching is not Catholic teaching, but in fact false allegation against the Church. One of the reasons why so many intelligent Protestants are coming into the Church is the fact that so many of them see through these false allegations.
Some will say that Catholics re-crucify and re-sacrifice Jesus again and again at every Mass and thus it is at odds with the words of Jesus one sacrifice for sins. Yes, this is a problem teaching, but not a Catholic teaching. This problem teaching is a Protestant teaching or misrepresentation of Catholic teaching not to be confused with Catholic teaching.
We do not teach that the offering of Jesus is a re-crucifying of Jesus at every Mass. We offer Jesus at every Mass because He asked us to do this in remembrance of Him.
- “Then he took the bread, said the blessing, broke it, and gave it to them, saying, "This is my body, which will be given for you; do this in memory of me" (Lk 22:19).
We do what Jesus asks of us and I don't think we should accuse Jesus of re sacrificing him self at every Mass, when in fact He asks us to offer Himself at every Mass in Memory of Him.
I find it interesting that even though the Catholic Church goes out of it's way to explain that we do not re sacrifice Jesus at every Mass it seems that no one is listening and so myth is continually perpetuated. However this is not always the case. I really like the commentary of Alan Latawiec who shares his journey from pervasive misunderstanding to the truth;
"I think this is the most pervasive misunderstanding non Catholics have about our teachings. Before I reverted, I actually believed it myself. Learning the truth - which nearly knocked me out of my chair- was one of the key markers on my journey home."
Welcome home Alan!!!