Why do we say "in range" but "out of range"?

Solution 1:

When you put an object, 'A', into a container 'B' you say that A is 'in' B. If you remove B from A you say that you have taken B 'out of' A.

I suppose the OP usage - 'in'/'out of' (range) is following this logic.

The same usage is found with figurative situations, for example 'luck' and 'favour'.

Solution 2:

The 'of' is a genitive of origin.

• In sight/out of sight
• In time/out of time
• In range/out of range
• Indoors/out of doors

Conceptually something is 'within' a containment. It is fixed in location. It is 'in' and no more need be said in order to fix it, conceptually.

But if it is outside of the containment, we require a preposition. It is not just 'out' as opposed to 'in'. It has become un-locatable because it is 'out of'.

The 'of' specifies that to which it has become un-fixed so that, now, we do not know where it is.

But we do know its origin. So we use a genitive of origin - 'of'.

EDIT I have just noticed @Dan 's answer and it seems I have, inadvertently, duplicated it, to some extent. Looks like we agree, anyway. (+1 to Dan.)

Solution 3:

If out doesn't require a complement, you don't need of:

(1) *I walked out of.

(2) I walked out.

If out requires a complement, the complement by default should be in the form of 'of + NP' unless the complement denotes not a space but a boundary, in which case the complement is more likely to be in the form of an NP:

(3) I walked out of the room. (space)

(4) %I walked out the room. (space)

(5) %I walked out of the door. (boundary)

(6) I walked out the door. (boundary)

Both (3) and (6) are well formed.

(4) is possible only in informal American English.

(5) is possible in British English but probably not in American English.

As for abstract nouns such as 'range', they denote a space rather than a boundary, and omitting 'of' sounds plain wrong.