Why do -car and -gar verbs in Spanish change spelling in the first person of the preterite?

This is what is classified as an "orthographic change". In simple terms, if the spelling was not changed the sound of the Word would be very different from other conjugations and the infinitive.

For example, if we look at a -car verb like "tocar" and conjugated it without doing the spelling change (e.g. incorrectly), the "yo" form in the preterite would be "toce" and pronounced like "toe-say". This changes the sound from the hard "c" in "tocaste", "toco" to a soft "c". By changing the spelling of the "yo" form in the preterite to "toque", it will be pronounced as "toe-kay", keeping the hard "c" sound.

The same issue applies if we look at a -gar verb like "pagar". If we conjugated it without doing the spelling change (e.g. incorrectly), the "yo" form in the preterite would be "page" and pronounced like "pah-hay". This changes the sound from the hard "g" in "pagaste", "pago" to a soft "g" - which sounds like an "h" in English. By changing the spelling of the "yo" form in the preterite to "pague", it will be pronounced as "pah-gay", keeping the hard "g" sound.