Curvature is one of the more recent tools Illustrator introduced (well, in 2014... time flies). Unlike older tools, it tries to be smart. One of this 'smart' behaviors is an ability to both select and edit paths. It prevents us from placing the next point of the currently selected path right above an existing unselected path — the tool treats it as an attempt to select the latter.

There is an existing request to tweak the continuation tolerance, similar to what Pencil has: https://illustrator.uservoice.com/forums/333657/suggestions/34578331

But to be fair, I’d love more options for the tool in general. So far it has ONE only, and it’s hidden within Preferences > Selection & Anchor Display: Enable Rubber Band... it should not be an app-level option! it’s a tool’s option! and it should be put in Curvature Tool Options dialog, called by Enter or double-click on the tool’s icon, just like every other tool allows...

And another option it should get must be 'Prefer selected path'.
With this checked, when nothing is selected — allow the tool to select path... but is something is already selected, prevent it from selecting, until I choose to. I’d even recommend to make this the default behavior.