Sympathetic Tension is one of the most important concepts for any guitarist, and especially beginners, to understand. If you don't know how to avoid it, it will begin to ruin your fingers and make finger control impossible, right from the beginning of playing.
Why do I tense up when I play guitar?
You're tensing up now because you haven't yet developed the right muscles for guitar playing. Simple as that. You're not really "pressing down hard" to fret notes or chords, it just feels that way because those muscles will be weak without exercise.