I thought the verb brauchen is a zu-construction verb, but in this context why does it have to be "zum Lieben" not "zu lieben"? Any explanations why it's like that?
Ich brauche eine Frau zu lieben
I need to love a womanif it were correct; however, in this sense
brauchen is only used for negation. The right sentence would be, I believe
Ich muss eine Frau lieben
Ich brauche eine Frau zum Lieben
I need a woman to love.
Using zum +
infinitive expresses purpose and means "for" or "to"
Meine neue Schuhe sind gut zum Rennen (=My new shoes are good for running)
Sein Kaffee ist noch zu heiß zum Trinken (=His coffee is still too hot to drink)
Dieses Feld ist groß genug zum Fußballspielen (=This field is big enough for playing soccer)
Note: The verb/infinitive is being used as a noun and as you know, nouns are capitalized in German, so that's why it's
zum Lieben not
Brauchen is first and foremost a regular verb that takes an object (noun, pronoun).
Ich brauche eine Frau.
It can be used in a zu-construction, if and ONLY if it is put into the negative. Whether or not the "zu" has to be there is matter of debate in contemporary German.
Du brauchst nicht zu brauen.
You don't need to brew.
Without the negative, brauchen can NOT connect with infinitives directly or via "zu".
Ich brauche zu lieben.
is wrong. Hence, you need to "nounify" the verb lieben and that's why it is "zum".