Why did God forbid Moses from entering the promised land?

A year before Joshua led the people into the promised land, Numbers 20:

1 In the first month, the whole congregation of Israel entered the Wilderness of Zin and stayed in Kadesh. There Miriam died and was buried.

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The older sister of Moses died.

2 Now there was no water for the congregation, so they gathered against Moses and Aaron.

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The Israelites tested (Ex 17:7) the Lord at the water of Meribah.

7 The LORD said to Moses, 8 “Take the staff and assemble the congregation. You and your brother Aaron are to speak to the rock while they watch, and it will pour out its water. You will bring out water from the rock and provide drink for the congregation and their livestock.”

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9 So Moses took the staff from the LORD’s presence, just as he had been commanded. 10 Then Moses and Aaron gathered the assembly in front of the rock, and Moses said to them, “Listen now, you rebels, must we bring you water out of this rock?”

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He did not speak in humility. He did not give glory to God. He was showy:

11 Then Moses raised his hand and struck the rock twice with his staff,

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The LORD instructed Moses to speak to the rock, not to strike it. Moses failed to follow God's instructions.

so that a great amount of water gushed out, and the congregation and their livestock were able to drink.

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Regardless, the miracle still worked.

12 But the LORD said to Moses and Aaron, “Because you did not trust Me to show My holiness in the sight of the Israelites, you will not bring this assembly into the land that I have given them.”

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Num 27:

14 When the community rebelled at the waters in the Desert of Zin, both of you disobeyed my command to honor me as holy before their eyes.” (These were the waters of Meribah Kadesh, in the Desert of Zin.)

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The LORD found Moses' action as

1. disobeying his command,
2. a lack of trust in God,
3. a failure to demonstrate God's holiness to the Israelites.

As a consequence, God did not allow him to enter the promised land.

Soon after that, Aaron, Moses' older brother, died. The Meribah incident was bookended by the deaths of Moses' sister and brother. It was the passing of the old order. It's a dramatic narrative composed of Moses' personal loss, communal crisis, and divine judgment.

Later, Moses recalled the incident in Deuteronomy 4:

21 The LORD was angry with me because of you, and he solemnly swore that I would not cross the Jordan and enter the good land the LORD your God is giving you as your inheritance.

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Centuries later, in Ps 106:

32 They angered him [the LORD] at the waters of Meribah, and it went ill with Moses on their account, 33 for they made his spirit bitter, and he spoke rashly with his lips.

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The palmist blamed the people for making Moses lose control over his speech. Moses reacted to the people's testing God improperly. God judged even Moses.

Was it a harsh judgment?

Yes, Moses was held to a higher standard as a leader. Teachers will receive a stricter judgment.