The simple answer is because that is the way it is laid down in Bunreacht na hÉireann [the Irish constitution] in 1937.

Article 12 of the Constitution lays out the title and duties of President [Uachtarán] and states :

There shall be a President of Ireland (Uachtarán na hÉireann), hereinafter called the President, who shall take precedence over all other persons in the State and who shall exercise and perform the powers and functions conferred on the President by this Constitution and by law.

In the rest of the constitution the office holder is referred to as "President".

The title of Taoiseach is more clearly described as being in Irish. Article 13 describes the head of government as Taoiseach. The office holder is referred to as "Taoiseach" in the rest of the constitution.

The President shall, on the nomination of Dáil Éireann, appoint the Taoiseach, that is, the head of the Government or Prime Minister.

The President shall, on the nomination of the Taoiseach with the previous approval of Dáil Éireann, appoint the other members of the Government.

The reason for this is that the title of President went back before the Treaty of Dec 1921 when the title of President of Ireland was used by Sinn Féin and De Valera in 1921 after the establishment of Dáil Éireann in 1919 [the so called revolutionary Dáil] and the declaration of independence.