From what is written, it looks like the tutor was telling her to stop rejecting peoples' offers to hang out, as that would give her the opportunity to learn more about how to connect with other people. It's not clear that he was telling her to have sex with any guy who asked; that just seems to be how she ended up implementing it, possibly through a combination of heartbreak over the break-up, not understanding how to relate to other people, and what seems to be a fundamental lack of understanding of her own needs and desires: "All that was left were his instructions, 'Don't reject anyone', and me mindlessly following it."
And thank you so much, HEXyren, for putting this chapter together. It provides a critical piece of Meguro's backstory.