Why use "need not" instead of "do not need to"?

There are two verbs need, which mean the same thing but use different constructions:

1.

He need not be concerned.

Need I be concerned?

This need is sometimes called a modal verb (although others find this term inconsistent): it always requires an infinitive without to; it doesn't have do-support in questions and negative sentences; and the third person singular (he/she/it) doesn't have -s. This is the need in your example. It is of the same type as must, will, shall, can, may, help, and probably a few uncommon cases.

Modal need is slightly old fashioned. Except in negative sentences and questions, it is less common in modern writing, except perhaps in certain fixed expressions (though the need in if need be is a noun).

2.

He doesn't need to call her.

Do I need to call him?

She needs to call him.

You need him.

This is the more common need, a regular verb (no 'modal'). If it is used with another verb, the infinitive with to is used. It always has do-support. It can be used without another verb, with a direct object (you need him).