Phalanx V-formation...exploit?

[Watchman]

BTW, in the case of non phalanx spears, what are the horses afraid of?

Or is just the ease of someone PUSHING you off the horse that causes the "bonus" in that case?

AFAIK horses regard about anything that appears as a solid, unmoving obstacle as something to avoid; being animals evolved to survive danger by running away from it, they're understandably wary about footing and colliding with things.

That aside, long pointy things are generally useful against cavalry simply because they largely negate the height advantage the horsemen have, and potentially allow you to kill the mount before you're even within the striking range of the rider. It of course doesn't particularly hurt that spears also take rather little "elbow room" to employ, allowing the spearmen to form into quite dense blocks horses try to avoid and will have a very hard time breaking in the off chance they can be goaded into even trying. And then there's the possibility of "bracing" the spear on the ground (as explained earlier in the context of pikes - the basic idea works with any decently long spear) to receive a charging horse, in essence turning the same principles of momentum that make lances so effective right against the cavalry.

...and Square for Field engagements.

...which would actually be perfectly legit realistically and historically. The classic "hollow square" formation to avoid cavalry flanking was well known already in Classical Greek times, and phalangites were no worse at employing it when necessary.