Why do we say "to fall in love"? Is it something unwished for?

To fall is something involuntary, outside of our control, not necessarily unwished, but hardly something you can plan.

The expression "fall in love" as in being overwhelmed by love has been with us for a long time, and occurs eg in Edmund Spenser's epic poem The Faerie Queen, published in the 1590s.

Both Scudamor and Arthegal
Doe fight with Britomart
He sees her face; doth fall in love,
and soone for her depart
- subtitle to Book IV, Cant VI
(modernized spelling)

and also

But it in shape and beautie did excell
All other Idoles, which the heathen adore
Farre passing that, which by surpassing skill
Phidias did make in Paphos Isle of yore,
With which that wretched Greeke, that life forlore
Did fall in loue: yet this much fairer shined,
But couered with a slender veile afore;
And both her feete and legs together twyned
Were with a snake, whose head & tail were fast cõbyned.
Book IV, Cant X
(modernized spelling)

English language shed most of its prefixes, affixes, conjugations, declensions and stuff a long time ago and has to get by using word combinations and phrasal verbs. It seems to use "fall" to mark the incompleteness of volition. I believe other languages use other means to the same end.

Compare with Russian: "влюбиться" and "полюбить", that is vljubit'sja (to fall in love) and poljubit' (to come to love smn/smnth). Same root, but different prefixes and suffixes - used with a purpose.

In the first case, the language resorts to the prefix "v" (into, inside); next comes the root "ljub" (compare with German "liebe"), ending with suffixes and an ending, dissecting which is a headache. Of note is the reflexive particle "sja" (to myself; kith and kin of the English "self", same letter "s"). Adding this originally meant "doing to oneself the action that the verb is conveying", but depending on the presence of other elements came to mean a lot of things, like "to a full extent" (the whole of myself). This v + sja (the thrust and completeness-to-oneself) combination provides the emphatic and involuntary feel similar to "fall in love", to such a degree that a bevy of makeshift analogies were penned, like Vtreskat'SJA, Vturit'SJA, Vtjuhat'SJA, with over verbs, mostly nonce-words, spatchcocked between v and sja, with the same overall result – “to fall in love”.

"Poljubit'" (to come to love someone or something), on the other hand, uses the prefix "po": here it means "to initiate something". One may initiate something voluntarily or otherwise, but without "sja" it just falls short of conveying the "fall in love" sentiment. So, when one seeks to explain to a third person why he "came to love" that girl, citing her virtues, he will oftener opt for "pojubit'", and when one wants to say something like "Don’t know why, but I just fell in love with her”, he will tend to use “vljubit’sja”.

Moreover, when one is using “vljubit’sja”, one has to use the preposition “v” (towards, in the direction, inside). Just like with “falling in love”. Only you place it before the person with whom you fell in love with: “Ja vljubil’sja v Annu” (I fell in love towards, inside Anna). Compare: “Ja vrezalsja v stenu” (I drove into a wall). Same v+sja, same v, same fatalistic feel, hopefully not the same final result, though.

To top it all, one may say “Vlubit’sja po ushi”, that is “To fall in love up to one’s ears”. The same falling-drowning-involuntary feel, because one also may be po ushi .. in debt, say.

This is a vertically-oriented version of the Love Is Out Of Control metaphor theme.
To quote from the article:

When one talks about
- being enchanted by,
- falling in love with,
or
- being crazy about somebody,

one is using metaphor themes; respectively,
- Love Is Magic,
- Love Is Out Of Control,
and
- Love Is Madness (a subtype of Love Is Out Of Control),
to talk about humanity’s favorite mystery.

Less heady forms of love, such as long-term relationships, use themes like Love Is A Journey
(at a crossroads, a dead-end relationship, not going anywhere, on the rocks,
and Freud’s famous railroad/tunnel symbols).