The reason you mentioned is the main reason we do hafrashas challah and the most important reason. But there are a range of reasons. Off the top of my head
– The Rabbonim instituted that we take Challah even when not in Eretz Yisrael with most of the Jews living there so that it should not be forgotten from the Jewish people. (I think according to most commentaries it is currently a Mitzva D’Rabanan, but that could change in the next few years)
– Because Adam Harishon was “Chalaso shel olam” and Chava led him to sin, so we women atone for this by taking challah
– To take the gashmius act of making bread and raise it to ruchniyus- so we lift up a piece and say “harei zu challah” (Baal Shem Tov)
– To remind us of Hashgacha Pratis – that Hashem is watching us at all times and is the One Who gives us food (Rav Samson Rafael Hirsch)
– The Gematria of ??? =?? which is the first and last letter of the CHumash (Beraishis-Yisrael)
– Eres, dough, is from the same lashon as arisa, a cradle for a baby, to teach us that a father should start teaching a child “Torah Tziva Lanu Moshe” as soon as they start being able to talk. (Chasam Sofer)
?????? ????????? ??? ????? ?????
There’s more but that’s off the top of my head.