What class an instrument belongs to depends on how the sound is created, not what it's made out of. This is why a harpsichord is a string instrument (plucks the strings) and the piano is a percussion instrument (strikes the strings)
I agree with your first sentence, but not your second.
It's important to remember that we classify things into categories for REASONS, not just because we do. So a category is only as valid as it is useful.
One of the main reasons for classifying instruments in families is to express the similarities of technique and sound production between them. This is crucial for a composer or arranger, for example, to know how to write for them. You wouldn't for example write a slow unaccompanied melody in long notes for the piano (a percussion instrument) and expect it to be effective in the same way as it would on the cello (a stringed instrument).
The defining characteristic of stringed instruments in this sense is not that they have strings, it's that they can control the volume envelope of each note from beginning to end, like the voice or like woodwind and brass instruments. The defining characteristic of percussion instruments - and this is really important because it's what sets them apart from ALL others - is that the player's control is limited to the initial attack of the note (notwithstanding mechanical add-ons extraneous to the note production itself, like the piano pedal).
In this sense the harpsichord is most definitely a percussion instrument. So is the guitar - and that's what I was taught as a child doing music theory. Guitar and piano were in percussion.
In a practical playing sense too, you don't see pianos among string sections, written as part of the string section, or being doubled on by string players the way violinists and violists can sometimes play both instruments with minimal extra training. The piano in an orchestra usually sits with the percussion section. The guitar in a big band sits with the rhythm (ie percussion) section. There are reasons for this, because the
roles that the instruments play are derived from the way they make sound, and thus related to those of the other instruments that make sound in a similar way.
Topic: I am right and all of you are wrong.