Why are we not supposed to cut the sides of our hair?

Answer:

"You shall not shave around the sides of your head, nor shall you disfigure the edges of your beard" (Leviticus 19:27).

The word that is translated as "shaved" means to strike off with violence, and the word rendered "disfigured" in this verse means to ruin, batter, or destroy. Therefore, this verse is not saying it is wrong to get a haircut or to trim your beard but is forbidding the disfiguring of your looks by chopping the hair to make yourself look ugly.

This was a heathen practice to show that a person was in mourning. "He has gone up to the temple and Dibon, to the high places to weep. Moab will wail over Nebo and over Medeba; on all their heads will be baldness, And every beard cut off" (Isaiah 15:2). "For every head shall be bald, and every beard clipped; on all the hands shall be cuts, and on the loins sackcloth" (Jeremiah 48:27). God is forbidding making a display of a person's grief.

It is similar to what He stated in regard to fasting. "Is it a fast that I have chosen, a day for a man to afflict his soul? Is it to bow down his head like a bulrush, and to spread out sackcloth and ashes? Would you call this a fast, and an acceptable day to the LORD?" (Isaiah 58:5). Instead, Jesus, like the Old Law, commanded people not to make a show of their grief. "Moreover, when you fast, do not be like the hypocrites, with a sad countenance. For they disfigure their faces that they may appear to men to be fasting. Assuredly, I say to you, they have their reward" (Mark 6:16).

The Old Law did not forbid cutting the hair because priests were told, "They shall neither shave their heads nor let their hair grow long; but they shall keep their hair well trimmed" (Ezekiel 44:20).