why is love the greatest? [1 Cor 13.13]

I'm glad you asked. There are several reasons.

FIRST of all, the context is about spiritual gifts [1 Cor 12-14]. Paul's point is that the engine of all proper employment of the gifts is love. The gifts will not be needed for all time, but love will stick around.

SECOND, the nature of faith and hope is that they are not eternal. This is closely related to the first point. When we are forever gathered with God and His people, faith and hope will not be necessary. They are gifts in the present that work with love to sustain us until then. The temporal nature of faith and hope help to point to the permanence and greatness of love.

THIRD, the idea of the person of the Holy Spirit is closely tied to Paul's understanding of love [see Rom 5.1-5, Gal 5.22, Eph 4.1-3, etc]. Edwards, Augustine, and Gordon Fee do an excellent job showing this. Thus, love's enduring nature says something about God the Spirit.

FOURTH, isn't real love supposed to be perpetual by definition? Take it, Billy:

Love is not love
Which alters when it alteration finds,
Or bends with the remover to remove:
O no! it is an ever-fixed mark
That looks on tempests and is never shaken

Love alters not with his brief hours and weeks,
But bears it out even to the edge of doom.
If this be error and upon me proved,
I never writ, nor no man ever loved