I cannot prove I like turtles.
Does my like for turtles not exist?
Why can't you prove whether or not that you like turtles? Very often others through observation, have realized a person's passion for something simply by that person's interaction with the object of their affection. When one sings or plays an instrument, does the audience not know whether or not the musician is simply playing in a mechanical manner, or out of love and enjoyment?
Would not your hypothetical turtle terrarium that is inhabited by several turtles, plus the turtle books on your coffee table, plus your photos of turtles throughout your house, plus your turtle tattoo, plus your ability to talk about turtles all day long, not prove your adoration of turtles?
In other words, if someone claims that they love someone but constantly mistreats them, it is safe to say that that person's love for the other does not exist.