Why did the farmers of the constitution agree to in meet in private?

Answer 1

I sincerely hope you meant "the Framers."

Anyway, the Constitutional Convention was originally convened for the adjustment of the Articles of Confederation, the precursor to our current Constitution. The problem with the Articles of Confederation (AoC) was that they gave very little power to the central government, instead focusing on the individual states. Each state could have its own money, court system, and many other things, and there was little regulation. The Framers realized that this system could not last long with the States so deeply divided, and they also realized that the AoC were far beyond repair, so they decided to create an entirely new country charter. The reason the Constitutional Convention was kept secret is that the delegates thereto were delegated to amend the AoC, not throw them out the window and start fresh.

Answer 2

They wanted to work without interference from others and to be able to discuss the issues openly. Unlike today there was no "instant " news cycle or modern technology and they were able to accomplish the task. One important thing as well there were no political parties that they were held to. Yes, they did have views on how a government should be made, but they were able to compromise to create this document that is still in use.