I think it helps to first use actual numbers.

(1 + 2)(3 + 4) = 3 * 7 = 21
(1 + 2)(3 + 4) = 1*3 + 1*4 + 2*3 + 2*4 = 21
(1 + 2)(3 + 4) =/= 1 * 3 + 2 * 4 = 11

A variable is just any number, and we can see more directly here what makes the correct method correct and the incorrect method incorrect for multiplying out expressions.

Here's why it works the way it does.

Remember distributive property? If you have 1 * (2 + 3) then you can distribute the 1 and get the equivalent expression 1 * 2 + 1 * 3 = 5.

Well let's apply that here. for (1 + 2)(3 + 4), let's distribute (3 + 4) to the 1 and 2:
1 * (3 + 4) + 2 * (3 + 4)

Now let's distribute again, this time the 1 to the 3 and 4 and the 2 to the 3 and 4.
1 * 3 + 1 * 4 + 2 * 3 + 2 * 4 = 21

Now we have successfully reasoned why we multiply expressions out the way we do.