The story about Omar (RA) that is used to substantiate the abrogation of text:
What is the reference you found this text in?
This is a very brief translation:
Ibn Abbaas narrated that Umar said, "The most reciting of us is Ubayy and the most juristic is Ali. But we leave out some of what Ubayy recites, because he said, 'I do not leave out anything I heard from the Prophet (PBUH)', but God said, 'Whatever we abrogate...'"
Anas (ibn Maalik?) narrated similarly.
Umar's point is that he leaves out some of what Ubayy recites, because Ubayy recites everything he heard from the Prophet (PBUH) including what may have been abrogated, but abrogation can happen, Umar argued, based on 2:106.
This text also reports a third
pronunciation of ننسها
(We cause it to be forgotten), which I haven't read anywhere else, namely, تنسأها (you, Muhammad, forget it). That pronunciation was the way Sa`d ibn Abi-Waqqaas recited it. Such pronunciation implies that God is assuring the Prophet (PBUH) that if he forgets any revelation, God will reveal something similar to it to him later!
The author of this article replies to folks who deny the abrogation doctrine, saying that the circumstance of revelation and the context leave no doubt, since it was all about answering those who deny abrogation!
I beg to differ. The context and the circumstance of revelation are a reply to those who deny that the Quran abrogated the Torah. That does not automatically mean that the Quran abrogates itself.