From the time of my sophomore year in college, I have heard about the complexity and difficulty inherent in executing a successful teapot. “Phaw,” I scoffed, “the parts aren’t so hard to throw, and I’m good at centering. No biggie.” Right? I was so wrong.
Problem 1: Numerous assembled parts can become heavy. Tons-of-bricks-teapot + tea = unpleasant to lift.
Problem 2: Visual continuity of separately conceived parts (body, lid, spout, handle) is a difficult aesthetic process.
Problem 3: Warping of the body due to spout and handle pulling on the body during firing, trapping the lid forever.
Problems 4, 5: Glaze sealing the holes allowing fluid passage into the spout or glaze sealing the lid in place.
Problem 6: Successful glaze outcome. I have been progressing in this area concurrently.
And etc. I have been puttering on making teapots properly since I began the thrown pottery life, about 7 years now. I’m certainly not the best potter ever, so this duration may seem excessive, but I refused to put a teapot out there that did not satisfy my checklist for what I consider to be a successful teapot execution:
Proper overall weight, thin walls, good aesthetic relationship of all assembled/trimmed parts, nice pouring arc from spout, clean pouring cutoff, snug lid fit, and nice glaze job.

White stoneware teapot salt fired to cone 10, glazed with Ryan's Green-black. All parts thrown on the wheel except for the pulled handle.
I accidentally met all of these criteria while making a teapot for fun from a spare bag of white stoneware. It’s not absolutely perfect, and there are improvements to be made in future teapots, but this is a good prototype to lead the way.

Here's the other side of the same piece. Salt firing causes a lovely directional variation, and this glaze is quite responsive.