How does private benefit exceed social benefit? I've done economics for 3 months only, so bear with me.

If Social Benefit = Private Benefit + External Benefit

Then how is it physically possible that private benefit could ever exceed social benefit?

Someone told me that if there is an External Cost this reduces the social benefit, but why? If the Social Cost already takes the External Cost into account, why would the Social Benefit do the same?

If the Social Benefit and Social Cost are two different things then why do they both take into account costs and benefits?

I really do not understand the logic behind it and do not understand my teacher's explanation. Much help is needed.

Thank you.
The net social welfare can be written as $W=B-C$, where $W$ is total welfare, $B$ is the benefit, and $C$ is the cost.

Suppose we are interested in thinking about a negative externality that implies a social cost of $E$. Then we would have $$W=B-(C+E)=B-C-E.$$

Imagine if, instead of viewing this as a social cost, we interpret the externality as reducing the social benefit. The expression would then be $$W=(B-E)-C=B-C-E.$$

So the two ways of thinking about the world are completely equivalent and it is merely a naming convention whether we call the externality a cost or a reduction in benefit. I guess your confusion has come about because you heard people on different occasions using the different conventions, without being clear about which convention they were using.

The only thing that matters is that we don't double-count the externality by including it as both a cost and a reduction in benefit.