There's some selective memory going around here. Tierney is solid enough defensively most of the time, but he's been turned inside out by Mahrez, Salah, Adama Traore. He's not a Maldini type defensive machine that some of you are making him out to be.
Tavarez is worse defensively but you have to balance that against what he brings offensively. My biggest criticism of Tierney is that he's too one dimensional - get to the byline, cross, repeat. He is a great crosser but none of our forwards are good at attacking high crosses, so it's a wasted skill. Tavarez brings us more combination play, ball carrying and composure. He needs to cut out the constant long shots though.
Competition is a good thing. Arteta got it right to keep Tavarez in. Hopefully Tierney has been watching Nuno and sees what he's been lacking, and vice versa. I wouldn't be surprised to see Tierney start against United.
I don't disagree with the majority of what you've said but I don't think anyone's claiming Tierney is an elite level defender, he's not. He's above average but really good players will cause him problems defensively. That's to be expected.
There's a difference between that though and Tavares making just really basic errors in terms of positioning, decision making, concentration etc. The fact he's good going forward and fun to watch seems to gloss over all the basic defensive stuff he's not good at in a lot of people's eyes.
That bad mistake against Liverpool probably didn't affect the result, in a nip and tuck match against Man Utd a similar sort of mistake like that may well do and he has those basic mistakes in him at this stage of his development.