"That is far from fair---" Peleus started but he knew that here was not the place to have this conversation. "This is not the place for this." His intentions for Achilles had always been to make him a man. To know how to even hurl a spear which he would have never learned had he lived cloaked under the guise of a woman the rest of his life. Or burned by his mother in that fire before she could try and steal him away. He had take Achilles to Charon. Charon was the teacher that Peleus had not been, yes, but that was for his son's growth. To give him the best chance at being the kind of warrior a father could be proud of.
Weakness as it had been for his son was not acceptable. Peleus was never supposed to bury his son before he himself had been an old man. He was not supposed to watch his ashes scatter away into the ocean and have the prick of tears under his eyes where Thetis could see. That had been his reasons of not showing. In the end he would have broken down and she would have seen.