I agree with others that vector drawing quickly gets too limited in Photoshop and that Illustrator is a better alternative.

But I can't reproduce the problem. In Photoshop 2020 I can draw Bezier curves which are not closed. And if they are closed I can select an edge with *Direct Selection Tool* and delete it.

[![][1]][1]

Edit: Perhaps your problem lies in drawing a *Path* instead of a *Shape*. While having the *Pen Tool* selected, in the top tool bar try selecting *Shape* instead of *Path*.

[![][2]][2]


  [1]: https://i.sstatic.net/zopS4.gif
  [2]: https://i.sstatic.net/V3U3u.gif