I will try to answer without using any mathematical formula, as your question is just made of words, without any mathematical symbols.

You should know that the wave function of an electron in the $\ce{H}$ atom is normalized. It means that the integral of the wave function over the whole space is equal to $1$. And it must be equal to $1$.

If you add two of these wave functions from two $\ce{H}$ atoms, the integral of this sum will be $2$. This is forbidden. It must be $1$. So you cannot simply add two normalized wave functions, like the $1s$ in the $\ce{H}$ atom. You have to take one-half of the wave function of the first atom and to add it to one-half of the wave function of the second atom. This would produce a new molecular wave function whose integral is equal to $1$. It is nice. This new molecular wave function describes a sigma bond, designed as $\ce{H-H}$ in the Lewis model.

Now you have to use and combine the other half of these wave functions, without adding them. The only thing to do is to subtract them. But such a subtraction produces a point between the two nuclei where the obtained wave function is equal to zero. As a consequence, this molecular orbital is a antibonding orbital. And the integral of this antibonding orbital is also equal to $1$.

Hopefully the pure theorists will pardon me for having simplified the description of the problem. I should have spoken of the factor √2/2 instead of $1/2$

I will try to answer without using any mathematical formula, as your question is just made of words, without any mathematical symbols.

You should know that the wave function of an electron in the $\ce{H}$ atom is normalized. It means that the integral of the wave function over the whole space is equal to $1$. And it must be equal to $1$.

If you add two of these wave functions from two $\ce{H}$ atoms, the integral of this sum will be $2$. This is forbidden. It must be $1$. So you cannot simply add two normalized wave functions, like the $1s$ in the $\ce{H}$ atom. You have to take one-half of the wave function of the first atom and to add it to one-half of the wave function of the second atom. This would produce a new molecular wave function whose integral is equal to $1$. It is nice. This new molecular wave function describes a sigma bond, designed as $\ce{H-H}$ in the Lewis model.

Now you have to use and combine the other half of these wave functions, without adding them. The only thing to do is to subtract them. But such a subtraction produces a point between the two nuclei where the obtained wave function is equal to zero. As a consequence, this molecular orbital is a antibonding orbital. And the integral of this antibonding orbital is also equal to $1$.

Hopefully the pure theorists will pardon me for having simplified the description of the problem. I should have spoken of the factor √2/2 instead of $1/2$. I should have said that it is the square of the wavefunction that should have been integrated. I have tried to be understandable to a beginning student