In your own opinon what reason and why would you check call flop then lead out the turn?

If I turned the nut flush and thought you might not bet but would call a bet.

Seems like a very good bluffing line. Indicates a lot of strength.

Tons of reasons, but two examples of why villain might do that:

1. Villain has 5 5 and the flop comes:

4 5 J

Villain check/calls. On the turn, board reads:

4 5 J Q

Suddenly there are, first off, a lot more hands that can call a value bet, but equally a lot more hands that can suck out on the river with a gutshot or flush or whatever. So villain bets partly to get calls from AQ and KQ and QJ type hands, but also to charge any draws to see the river.

2. Villain has 7 6 and the flop comes

4 5 J

Villain check calls with the open-ender. On the turn, board reads:

4 5 J Q

Villain leads out partly as a semi-bluff with quite a nice draw, but partly to 'set the price' for the river -- villain makes a bet smaller than the one hero would probably make to try to get to the river more cheaply.

If I misclicked on the flop?

Kamikaze's example, imho, shows why it's usually a bad line.

For example, we assume that we had too much fold equity on the flop to make a x/r on the flop with 55 the most +EV line, yet when we have the OESD we didn't use that apparently large amount of FE to make a +EV x/r with our semi-bluff. At the same time, we rationalize that we have enough FE to make the lead with the OESD +EV, but when we have 55 we lead because 'more hands can call'. I don't know if there's a term for this common cognitive bias in poker but I call it 'hand bias'.. our view of villains range and frequencies are subtly affected by the actual hand we hold (and not because of combinatorics).

Chad's answer is the best so far IMO.. though also when we x/c the flop with a bluffcatcher and the turn card improves our hand but decreases the frequency with which villain will bet is a good spot to take the x/c, donk line.

I consciously called the player 'villain' and not 'hero' for that very reason.

And part of my point was that the bet sizing on the turn often gives you a good clue as to the reason for the bet.

I did notice the villain/hero thing but didn't put 2+2 together

Because we floated and then suddenly got our dream card and we're playing a calling station that we can't trust to build a pot by betting again?

This is called a donkbet, and there's virtually never a good reason to do it, especially on the turn. You probably make all worse hands fold, and all better hands call/raise. The only time I might do it is if I was against a ridiculous monkey calling station, I hit a big hand on the turn, and I simply had to build a big pot quickly.