And true love is only proven over time. Any relationship more than a few months old (whether familial, marriage or friendship) has a few scars. You can't be in any meaningful relationship with another human being for any length of time without them hurting you. And as the relationship ages, the number of wounds inflicted by the other party grows (as is natural).
Have you ever had a friend who routinely hurt you? Over time, the natural inclination is to ask yourself why it is you remain in that relationship. The simple truth is love. You do your best to heal the wound together, then you place that trust back squarely in their hands, and you walk on together.
The depth of your love, paradoxically, is proven, in part, by your willingness to, when injured, push past the pain, join hands with the one who has injured you, and through your actions, demonstrate your undying trust in them.
It's like God's love for us. There's something about God's love that sees past our constant failures. There's a song that says it well, I think:
A thousand times I've failed
Still your mercy remains
And should I stumble again
I'm caught in your grace.
Your light will shine when all else fades
Your glory goes beyond all fame.
-From the Inside Out, Hillsong United