Why was it agreed that two-thirds and not some other fraction of both houses were allowed to call a convention for proposing amendments to the Constitution?

The Amendment Process (outlined in Article V) is meant to be drawn-out and complicated. The Founders made it this way because they didn't want the Constitution to be confused with common legislation and wanted to keep it as higher law (we see this in the supremacy clause of Article 6, clause 2). There are three subsets of majorities: a simple majority (or half plus one - over 50%), a super majority (or 2/3), and a super super majority (3/4). The simple majority requirement for propositions for amendments would make it extremely easy for an amendment to get proposed (especially contemporarily with all the party politics), and therefore would not fall into line with the "higher law" ideal of the document. a super super majority (3/4) would make it too complicated for a proposal to pass, and could prevent necessary and vital amendments from every being ratified, therefore, the super super majority is only used for ratification of amendments, to ensure that the amendment is necessary and appropriate. Therefore, the super majority of 2/3 was decided upon making it not too simple, yet not to complicated to propose amendments, ensuring that the proposal was valid enough to pass with 66%.