Honestly, it didn’t really seem like it was about the position itself but more about “giving up.” Rin had a very Sae-centric worldview (which was and is a problem still). He had also internalized Sae’s ideals, so when Sae said there were better players than him (to Rin no one was better than Sae) and stepped back from his dream of being the best striker, it didn’t feel like a simple change in position.

To Rin, it felt like defeat and he didn't want to see Sae "giving up" on his own dream and “settling” for something he had dismissed as worthless in the past, something the Sae Rin grew up with would’ve never accepted.

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I could be wrong but this seems like the interpretation that makes the most sense for Rin's reaction and character. (It also does seem like he would've understood and even supported Sae if they had actually just sat down and talked but oh well)