Why was Aaron not allowed into the promised land?

Moses and Aaron did not go into the Promised Land because that was God's will for them. Caleb and Joshua went into the land because they had faith and trusted the Lord. Of course Moses had sufficient faith to be saved, but the Lord chastened him with an earthly discipline... he went to Glory but not into Canaan.

The previous posts are all good. It could be added that Aaron and Moses are personifications of the Moral and Ceremonial Law and the Promised Land is a picture of Heaven or of the Kingdom of God.

Moses and Aaron did not lead the people into the Promised Land is a hint that it is impossible for obedience to the laws of Moses to save us. There will always be some sin that ruins us. Moses was forbidden to enter the Promised Land because of just one sin. And so it is with us: just one sin is enough to ruin us too (so how complete is our utter ruin!). "Cursed be he that confirms not the words of this law to do them." (Deuteronomy 27:26) And "Cursed is everyone who does not continue to do everything which is written in the book of the law to do them." (Galatians 3:10). Moses and Aaron fell under this curse of the law too (so they too needed to be [and of course they were] saved by grace).

The only way to enter our Promised Land is the way of Caleb and Joshua, by faith. The just shall live by faith (Romans 1:17, Hab 2:4, Galatians 3:11).

Moses and Aaron did not enter to hammer home the truth that the law will only get you into Heaven by a full-hearted, total, life-long obedience, without a single sin, i.e. if your walk with God is better than that of Moses and Aaron, but for all us ordinary mortals the only way is faith in Christ (John 14:6) who "died for our sins" (1 Corinth 15:3) (and the resulting repentance).

The 40 years of wandering in the wilderness was the longest death march recorded in history, every Israelite over twenty years of age when they left Egypt under Moses’ leadership died in the wilderness, except for three people: Moses, Joshua, and Caleb (see Numbers 14:38)

During their forty years of desert wandering, the children of Israel alternately blessed and cursed the name of God. When He showed them miracles, they humbled themselves. When the tests and rigors of desert life became difficult, they hardened their hearts in anger and resentment. They forgot His power and trembled in fear at the thought of facing the Canaanites. In so doing, they lost their privilege to enter the land of promise.

Arron was Moses' older brother. His age was his misfortune in not reaching the promised land. He simply couldn't outlive all of the house of Israel, and passed away from old age while waiting for everyone who had lost their privilege to enter the land of promise to finally die off.

Numbers 20:12 But the LORD said to Moses and Aaron "Because you did not trust in me enough to honor me as holy in the sight of the Israelites, you will not bring this community into the land I give them."

Aaron's death was a judgement for what happened at the water of meribah.

“Aaron will be gathered to his people because he will not enter into the land which I have given to the children of Israel because you rebelled against Me at the water of Meribah.” (‭‭Numbers‬ ‭20:24‬ ‭MEV‬‬)

The water of Meribah refers to the spring that flowed from the rock that Moses struck. God told Moses and Aaron to speak to the rock to make water flow from it, but instead Moses struck it with his staff.

Moses and Aaron went from the presence of the assembly to the door of the tent of meeting, and they fell on their faces, and the glory of the Lord appeared to them. The Lord spoke to Moses, saying: Take the rod, and gather the assembly together, you and Aaron your brother, and speak to the rock before their eyes, and it will give its water, and you will bring out to them water from the rock; so you will give the assembly and their livestock drink. So Moses took the rod from before the Lord, as He commanded him. Moses and Aaron gathered the assembly before the rock, and he said to them, “Hear now, you rebels. Will we bring out water from this rock for you?” And Moses lifted up his hand, and he struck the rock twice with his rod, and plenty of water came out, and the assembly drank, and their livestock. The Lord spoke to Moses and Aaron, “Because you did not believe in Me, to sanctify Me in the eyes of the children of Israel, therefore you will not bring this assembly into the land which I have given them.” This is the water of Meribah because the children of Israel argued with the Lord, and He was sanctified among them.” (‭‭Numbers‬ ‭20:6-13‬ ‭MEV‬‬)

Aaron was called to be a priest and kind of spiritual helpmate to Moses. It was his position to uphold Moses and to support him. Though Aaron did not himself strike the rock, he was there when God commanded them, and he allowed Moses to falter, sharing in his disbelief.