Max and Deborah had one thing in common, they were both in love with Noodles. Max always slept with the women that Noodles had had first. Max's feelings towards Noodles were pseudo-homosexual, no doubt about it. Max takes as his mistress Noodles' first 'rape' victim, Carol. And then years later he gets together with the love of Noddles' life, Deborah, who is also one of Noodles rape victims, but more of that later. Max is able to feel sexually close to Noodles by having sex with the women that Noodles has had sex with first (forced or otherwise). This is the closest thing to physical intimacy with Noodles that Max will ever get.
Noodles loves both Deborah and Max, but he feels more of a sense of loyalty to Max and this is why he always chooses to stand by Max, even at the expense of Deborah. Twice in this film, both as a child and an adult, Deborah taunts Noodles with the words "Mama's calling.", meaning that Max wants Noodles at his side. Deborah is hurt that Noodles always chooses Max over her, and ultimately this is the REAL reason that she decides to follow her ambition and go to Chicago, she is angry and upset that SHE is not number one in Noodles loyalties and priorities, Max is and Deborah feels that she will always be competing with Max for the attention of Noodles. This is also the reason that Deborah and Max have never liked each other, they both love Noodles and there is a deep jealousy between them, because they BOTH want Noodles.
Max of course can never reveal to Noodles how he really feels about him, perhaps Max does not even realise himself that what he feels for Noodles is sexual love. This is the reason that utimately, Max and Deborah get together later in life, their shared love of Noodles is what draws them together, and keeps them together, despite the fact that they previously did not like each other. By being together it is as if they can keep alive their memories of Noodles and the deep love that they still both feel for him.
As for Noodles, he is a much simpler character (at least he is, compared to Deborah and Max). Noodles is a thug, plain and simple. When he makes his fortune, he believes that this will convince Deborah to marry him and MAYBE she would have if he had been prepared to choose HER instead of Max and the gangster life-style; but Noodles is not a hugely intelligent individual and he blows his chance with Deborah by not putting her first.
He takes her on a date, and in the back of a limousine, Deborah tells Noodles she is going to Chicago in search of stardom. Noodles is devastated, crushed. He has loved this girl since he was a kid, and finally, just when he thought she was within his reach, he is going to lose her again. He is so deeply hurt, and so angry that his love is going to be leaving him, probably forever, that for a moment he is in the grip of some kind of madness. Deborah is startled. She has never felt such anger and coldness from Noodles, and she doesn't like it, she wants them to part as friends so she leans in and gently kisses him. This is too much for Noodles, he is getting mixed signals from Deborah (he believes). First she is rejecting him, and then she is kissing him. Noodles is confused......does Deborah want him to make love to her?
Now remember, Noodles is not very intelligent, and he has been brought up with absolutely no idea of how to treat women. He has spent his most formative years in a borstal and a prison, and he himself committed an act of murder when he was little more than a child. His experiences with women have been limited to prostitutes or with women like Carol, the blonde cashier who encouraged him to rape her because she is a masochist who enjoys extremely rough sex; the scene in which Carol entices and provokes Noodles in to raping her ends with her having a screaming orgasm. So now we have Noodles in the back of a Limo with the pure and innocent Deborah, and he is thinking that she is 'asking for it' as well.....and so he rapes her in the most brutal and horrific fashion. But he discovers that Deborah is most certainly not like Carol, or the young prostitute Peggy, Deborah is definitely NOT ejoying what is happening, Deborah is certainly screaming, but not with pleasure. Noodles is genuinely puzzled by Debbie's 'strange' reaction, and this is why he carries on with the ghastly rape, he figures that if he 'keeps going' and 'gives her a bit more' she will start to enjoy it like Carol did, poor, ignorant, foolish Noodles.
Only later does he realise that he has ruined whatever chance he ever had with the love of his life by this one revolting and despicable act. For her part, Deborah moves on with her life, but there is a part of her that will never stop loving him because she also realises, deep down, that Noodles has suffered more from the act of raping her than she herself has. Noodles life was in ruins from the moment he raped Deborah, and he was never truly happy again. He had hurt and violated the one person that he loved more than anyone else in the world and this is the reason that Deborah is very easy on him when he turns up in her dressing room all those years later, she doesn't scream or rage at him because she knows he has already suffered a life sentence of regret for what he did to her and she has finally forgiven him.
As for Max, he has wealth, fame, position, he has Deborah and they have a son together named David, who is undoubtedly named after Noodles, whose real name is of course David Aaronson. And yet, Max is not happy. How can he be, when he betrayed the only person he has ever deeply and truly loved? His friend and the love of his life, Noodles. This is the reason Max wants Noodles to kill him, it is his way of saying to Noodles, you can kill me for what I did to you but please forgive me first.