Why use lower F stop?

[KmH]

It takes more than a large lens opening to blur a background.

You also need an appropriate focal length and an appropriate point of focus distance.
The closer a background is to the subject, the less blurred the background will be.

FWIW - f/2 is a bigger number than f/16 is, because they are fractions. f = the lens focal length.

So a 100 mm lens set to f/2 has a lens aperture that has a 50 mm diameter - 1/2 the lens focal length.
A 100 mm lens set to f/4 has a lens aperture that has a 25 mm diameter - 1/4 the lens focal length.

A 50 mm lens set to f/4 has a lens aperture that has a 12.5 mm mm diameter - 1/4 the lens focal length.
A 50 mm lens set to f/2 has a lens aperture that has a 25 mm diameter - 1/2 the lens focal length.

Here comes the curve - f/2 lets in 4 times (2 stops) more light than f/4 does, because the area of the lens opening has increased more than the aperture diameter between f/4 and f/2. How much the aperture area changes can be calculated using the square root of 2 - 1.4142..
So 2 x 1.4142 = 2.8 and f/2.8 lets in 1/2 as much light as f/2 does. Or going the other way - f/2 lets in 2x more light than the smaller lens opening f/2.8 does.