Erratic check engine light that indicates a bad catalytic converter

For the last 25,000 miles, I have had a check engine light that periodically comes on and at first it would even then go off on its own. Now it does stay on till it is cleared, then it will stay off for a period of time then it stays on constantly till it is cleared. The Honda dealer says that it is a catalytic converter that “is going bad”. I took it to another mechanic who said that it might be a dirty air filter; the air filter was replaced and the light stayed off for a period, but then came back on. My question is, has my catalytic converter gone bad at only 100,000 miles plus or is it something else? Also the Honda dealer says that if I replace the converter with an after market brand that the check engine light will continue to stay on. Is this true or are they just trying to sell Honda parts?