If you don't change the direction on a flate plane, the line you're forming will be straight, not go in a circle. The appearance of a straight line that actually goes in a circle (or which veers from a straight line at all) is only possible in non-euclidian geometry, which is only possible if the plane is curved. If the line is straight, one would move toward the edge of the plane. You can only remain on the plate if the line in which one moves is bent ever so slightly. Why would the line bend, and moreover, why would it bend so much as to form a circle? The only way to go in a straight line on a plate and still move in circles, is if you're on the inside rim of a bowl and your ground makes a 90 degree angle with the ground in the centre (i.e. the rim is vertical). But a bowl is likewise a curved plane.
If you'd somehow move in circles without noticing, you'd always keep on measuring a 90 degree angle between your direction and the north pole. That's also incompatible with a flat plane: the angle would increase and eventually approach 180 degrees. How would you explain why it remains 90 degrees?
In the latter part of your post, you're giving a counter-argument, which is actually slightly lower on the pyramid of debate. (I'm talking about how curvature isn't observed directly.) I'm not addressing that right now because I'd like to establish first that the Earth isn't flat. After all, whether the Earth is a globe or a flat plane are separate matters: pointing out a problem with one theory doesn't establish the veracity of the alternative. All I'll do is mention that the curvature can be observed at shore, because when a ship arrives at the horizon, the mast is observed first, and only afterward the hull. This is how the ancient Greeks concluded that the Earth is spherical.
If you don't change the direction on a flate plane, the line you're forming will be straight, not go in a circle. The appearance of a straight line that actually goes in a circle (or which veers from a straight line at all) is only possible in non-euclidian geometry, which is only possible if the plane is curved. If the line is straight, one would move toward the edge of the plane. You can only remain on the plate if the line in which one moves is bent ever so slightly. Why would the line bend, and moreover, why would it bend so much as to form a circle? The only way to go in a straight line on a plate and still move in circles, is if you're on the inside rim of a bowl and your ground makes a 90 degree angle with the ground in the centre (i.e. the rim is vertical). But a bowl is likewise a curved plane.
If you'd somehow move in circles without noticing, you'd always keep on measuring a 90 degree angle between your direction and the north pole. That's also incompatible with a flat plane: the angle would increase and eventually approach 180 degrees. How would you explain why it remains 90 degrees?
In the latter part of your post, you're giving a counter-argument, which is actually slightly lower on the pyramid of debate. (I'm talking about how curvature isn't observed directly.) I'm not addressing that right now because I'd like to establish first that the Earth isn't flat. After all, whether the Earth is a globe or a flat plane are separate matters: pointing out a problem with one theory doesn't establish the veracity of the alternative. All I'll do is mention that the curvature can be observed at shore, because when a ship arrives at the horizon, the mast is observed first, and only afterward the hull. This is how the ancient Greeks concluded that the Earth is spherical.
How would you measure if you are going straight?