Why is Big Mom afraid of Shanks? Why is Big Mom afraid of Shanks? Is it because of his ultimate Haki? Or is it because of the fact that he even survived after clashing with Edward Newgate and getting in a war with Kaido?
Big Mom is arguably the weakest Yonko, but she makes up for this by forming allies with different nation. Hence, the numbers of her offspring.

Shanks is definitely a force to be feared for good reasons.


He has only 1 ship - As we currently know, Shanks only has a caveat of a crew in 1 single ship and that says a lot. Numbers in the OP world can mean a lot and him being in the New World with just a single ship and exceptional crew members who are known to be great at Haki (Beckman, Lucky Roo and Yasopp).  
Former Cabin Boy of the Pirate King, Roger - He was known to be a part of Roger's Crew with Buggy, although this doesn't mean much because of the latter's credibility, being part of the crew might help him develop his Haki.
Haki Strength - Shanks is shown to be a master of 2 types of Haki, Armament and especially Conqueror's Haki, greatly depicted when he boarded Whitebeard's ship. He also used to occasionally fight with Mihawk, the World's Greatest Swordsman before his arm got severed. 


Just these three alone would make you fear the red-haired Pirate. Also, he interrupted Kaido's attempt to attack Whitebeard during the Battle of Marineford and stopped said battle by just announcing the war is over which prompted Sengoku to do it which proves that Shanks is definitely someone you don't mess with.

If he can stop Kaido, the World Government/Marines, and make Blackbeard shiver then this just proves my point.

TL;DR Big Mom is afraid of Shanks because he's just too powerful for her.