When we made our First Communion we were told not to chew. Really the host should not come in contact with the teeth. It should be allowed to dissolve as much as possible and if it sticks to the roof of your mouth it shouldbe rolled off with the tongue and swallowed.
Chewing it with your teeth leaves room for parts of the host to become stuck to the teeth or between the teeth and that leaves room for the host to touch something profane.
It boils down to a realisation of just what the Sacred Host actually is.
Rev. George Searle (a Catholic priest) who wrote How To Become A Catholic also has the “imprimatur and nihil obstat” (a certification that the given work has been inspected and there is nothing contrary to faith or good morals), so when he gave instructions on the eating of the Eucharist, he had the approval of the archbishop. Deharbe’s Catechism, No.1, 273 agrees with Searle:
“Do not keep the Sacred Host [God] in your mouth until it is quite dissolved; but let it moisten a little upon your tongue, and then swallow it.”
It is the belief that every particle of the host, no matter how small, contains the “whole and entire Christ”:
“…for Christ, whole and entire, exists under the species of bread, and under each particle of that species” (Council of Trent, Sess.xiii, cap.3). Therefore if you chewed Jesus, you would divide the bread in your mouth into several pieces, each one containing the “whole and entire Christ”.