When Feyre stayed with the fey who had his wings torn off that was one of the first very personal moments that her and Tamlin shared. It was when she apologized for killing Andras and it was when she gave her speech about not wanting to die alone. It was also the moment where I think she started to view fey as something more than the enemy who deserves to suffer.
Fast forward to when Rhys interrupts their meal and officially meets Feyre. He goes through her mind specifically looking at her thoughts about Tamlin. I think he found that first pivotal moment between the two of them and it impacted Rhys a lot. Here is this High Lord, who is lonely because everyone thinks he’s Amarantha’s loyal bitch and is unable to fly, something he loves to do, because he fears it will be taken away from him permanently. I’m positive that Rhys was probably there for that fey’s torture and seeing a human girl, who hates fey, mourn over that broken body hits close to home.
Now we’re under the mountain, Feyre has the tattoo and is connected to Rhys in a way that now she’ll never be alone. Amarantha is killing her and Rhysand is freaking out even though it seems like there is nothing left that Feyre can do to help him stop her and yet he still wants to save Feyre. Not because of selfish intentions but because he likes her and when Feyre dies it’s Rhys, with his tattoo and mind connection, that makes sure she isn’t alone.
When they’re out on the balcony she asks him why. Now mind you, Rhys has been stuck beneath Amarantha for more than 50 years and he tells her how he wanted his offspring to know that he fought her at the end. But realistically, it looked like Feyre was useless when he attacked Amarantha. There were other’s trying to usurp her behind her back that Rhys knew about. (Remember when he broke that fey’s mind against Amarantha’s wishes to protect the High Lord’s plan?) He could have stood at the sidelines and watched Feyre die and try to overthrow her with the other fey that were resisting but he didn’t. He fought back when all looked lost for Feyre. So when he says all that stuff about being part of the legends I think that was true before he met her. But when Rhysand says “I didn’t want you to fight alone. Or die alone.” It was the answer to why he chose that moment. It wasn’t because he thought that Feyre could still save them. No, instead he chose to stand up to Amarantha for the human girl who cried over the fey who lost his wings, for the human girl that understood him, for the human girl who showed more bravery than most of his kind. That is why Rhysand choose that moment to fight.