I am traveling to Ireland with Dual Citizenship which passport do I use?

You always use the passport of the country you are entering or leaving.

You need to present your U.S. passport when you leave and enter the U.S.; you need to show your Irish passport when you enter Ireland.

That's how dual citizens travel all the time. There will not be a problem entering Ireland; lots of Irish people lose their passports overseas and re-enter their country with a new passport that has never "left" Ireland.

Your Irish passport should be used to enter and leave most countries in preference to your US passport particularly in the EU. The fact that you have never entered Ireland on this passport is not a problem. Ireland allows citizens to hold as many passports as they wish.

Your US passport must be used to enter and leave the US.

You enter/leave the country using that countries passport or you are entering and due to immigration checks and immigration controls as a non citizen