She even gives him an ultimatum, which, in this situation, is extremely selfish. “Which is it? A memory or us?” To refer to a cherished individual as a mere memory is just wretched in my honest opinion.
Oh man, I have some serious issues with this. She wasn't telling Cloud, chose Aerith or chose us. She was saying, "Are you going to allow your feelings of guilt get in the way of you being alive and the people that are willing to accept you."
Keep in mind what was happening here, Cloud isn't mourning. Cloud has given up on everything. At this point, us or your guilt isn't just a philosophical question, it's a literal question.
Marlene has just been captured by the enemies. Denzel and other children have been kidnapped by these same guys. And one of these guys beat Tifa to the point of unconsciousness so it's a reasonable assumption that Cloud is the only person who could defeat them. And he was going to walk away from the situation, like he walked away from his family when it got too hard.
He was going to leave the children they were raising in eminent danger. There's not a mother in the world that would take that sitting down.
At this point, someone needed to tell him, it's time to chose. He needed to stop running away from the hard questions. Tifa has in fact, supported Cloud through a ton of his moodyness, guilt, and struggle to find happiness. But supporting them does not always mean allowing him to waste away.
Aerith does also support him in her own way, much different from Tifa's. But the roles aren't meant to be the same. Aerith is the spiritual side of the planet, a healer, and the woman who can give him forgiveness. Tifa is Cloud's rock, who is by his side at his worst and they grow to be stronger characters together.
Tifa doesn't want Aerith to leave the picture, Tifa want's Cloud not to be consumed by his feelings to the point he cannot live anymore. She smiles up at the rain fondly saying that Aerith was always there for him, and thanks her. That's not the mark of a woman who wants Cloud to forget her, that's the mark of a woman who wants him to move forward.
“Look at you, you think you’ve got it so damn hard!” That’s not what he’s upset about! He’s in a state of mourning and fear! Losing loved ones is hard! Of course you want him to move on, that’s understandable, but forcing him to put a smile on his face won’t be what gets him back on his feet. Healing takes time, and longer for some.
She knows what the real problem is, she explicitly states it later on, "You're scared of letting people down." This is at the core of everything, Complete even has an extra scene where he imagines Zack and Aerith's deaths right before he saves Tifa and Denzel.
Healing takes time and she knows it because Case of Tifa shows that she has allowed Cloud his space and time while trying to talk to him about it. But it's something that he needs to be able to confront. Cloud wasn't confronting it, he was going to lay down and die. This is mentioned specifically when Tifa and Marlene meet up at the church.
And guess what, Cloud manages to push past it. Not just because of Aerith like the analysis would have you believe, but because of everyone. Tifa, Marlene, Vincent, Aerith.
“With the support of former allies and Tifa, an important woman to him and now also part of his family, Cloud regains the courage to move forward.” -Cloud Strife Compilation FFVII Ultimania character profile.
Hell, look at the moment when he goes to defeat Bahamut, the very moment where he finally goes into the fight with all his conviction, he cannot reach the enemy on his own and his allies, including support from Aerith, help him reach where he needs to be.
When he fights Sephiroth, Tifa is the one that tells her comrades (and the audience) the part of Cloud that he lost on his way, his courage and conviction, and he was gaining it back when he fought Sephiroth.
Cloud in AC/C wan't fully him. That was the part that was so consumed with negativity that he was willing to let him and others die because he couldn't face the reality that was facing himself. This isn't new. Tifa had her own problems in CoT- her own guilt and questions of what's next. Barret's burden of finding his place in life without violence. Red XIII's coping with the mortality of the people around him. And this is Cloud's turn.
AC/C was never about Cloud/Tifa or Cloud/Aerith. This was his "Case of" story, where Cloud had been drowning in despair and unable to know a way to move forward. And through his own power, and the support of the people that have loved him: Tifa, his family, Aerith, and Zack, he found his way again. And without all his doubt and fear weighing him down he was able to finally return to his family, quite happily. Even the latest "The Kids are Alright" novel has Cloud mentioning his family at the end.
The promise land wasn't the church. It wasn't a location even. It was with the people that he loved. His family, his comrades, and even Zack and Aerith who were watching him. If you frame it as a Cloud/Aerith movie, then yeah, I understand why you would think it was the church. But it wasn't, it was about Clouds strength and his relationship TO EVERYONE. Cloud has important scenes with Aerith yes, but Zack as well, with Tifa, with Denzel, and with Marlene.
Tifa needs a protector to fit into her princess desires. She needs a knight in shining armor who can make her laugh and remind her that she has no reason to be afraid to share her feelings.
lolololol forever.
Tifa is a caretaker, who looks after children that are not of her own, one that was terminally ill. There are romantic notions of "saving" but they are pretty much gone. The point of Cloud/Tifa that it isn't a fantasy. It's real, it's hard, and it's absolutely worth it.
Tifa loves Cloud and it has nothing to do with princess notions. In almost every scene that matters focused on reality, it was about her supporting Cloud, making sure he was okay. You can't convince me that Tifa only wants the princess ideals when she forgo the world to support a Cloud that practically a vegetable and probably wiping the drool off his face. She had wanted to be saved but in VII and beyond never expected it, and barely mentioned it unless it was to remind them of earlier times.
Her mind wasn't changed when Cloud was mentally broken. Or when he wasn't in soldier. She started their relationship in VII knowing that there was something wrong with and decided to look after him. That's the exact opposite of wanting him to save her.
“Apart from being Cloud’s childhood friend, she is also the woman who understands him all too well and devotedly supports the mentally-weak side of him.” - Tifa Lockhart Compilation FFVII Ultimania character profile.
edit:
oh god this post is ryu long what have I done???
Edit II:
I don't have enough time for the words in my head to write all the issues I have with Denzel being Cloud and Aerith's child, and that problems that has with not only the family dynamic but with Denzel, who has his own story- all his parental figures that have come and died- and own character development- and the problems this creates with Tifa's own arc with Denzel.
I think they did this precisely because they didn't want to upset C/A fans. 
