>>49686709I imagine daitengu (who are often syncretic with mountain kami in Japan, which is a case for tengu behind Megumu) would probably engage in active diplomacy or even polite friendships with more important kami on Youkai Mountain. Kanako is a major league that talks with Tenma, Aki sisters or Hina are generally small fries, but someone like Chimata or Kutaka could be seen as equals even by proud tengu standards.
All of this above to say that Megumu could have given her egg for Kutaka to hold in the same way many mothers let their female acquaintances play with their baby children for a while. A little bit of trust, a little bit of showing off, a little bit of shared happiness, maybe even to inspire some pang of jealousy.