Is capital always a liability?

Capital is an asset

Capital is never a liability

Capital is an asset. The lack of capital is a liability.

The accounting equation is, "Assets = Capital + Liabilities."

It can be stated other ways. "Capital = Assets - Liabilities."

That's where the "balance" in Balance Sheets comes in.

If you understand what "equity" is in a house, you understand the most basic of how a balance sheet works. If you have a house you bought for $100,000, put down $20,000, and took out a mortgage for $80,000, your balance sheet would look like (assuming no other assets or liabilities):

Assets: $100,000

Liabilities: $80,000

Capital (sometimes referred to as "equity") $20,000

ie, Assets = Capital + Liabilities

Capital is not a liability account. It's an equity account.

Capital has a credit balance but that does not mean that it is a Liability.

Read your assignment. Capital, in general, is not a liability. If a company takes on liability to raise capital, then in a way the capital is a liability, but not really. You need to understand the points your instructor is making and learn in class.