[LocalH]

The most basic method is to "bob" deinterlace, which is more of a form of "interlace simulation" - you take the original fields, place each one in the appropriate image lines of a separate frame of video, then perform some type of interpolation of each frame for the in-between lines. More advanced algorithms exist like yadif, that do some amount of motion detection to determine which parts of the image require deinterlacing, and which parts can be essentially done with a "weave", which is just taking part of the image data from a combined 30fps frame containing two fields.

[ErroneousBosh]

Okay, so what you're doing there is averaging the information between the two fields.

That gives you 25fps. It can only ever give you 25fps.

There are 50 fields per second, for 25 frames per second.

If you average the odd and even fields, you get 25 frames per second.

[LocalH]

Untrue.

Let's suppose we fill odd fields with black, and even fields with white.

The end result when played back on a CRT will be the entire screen flickering between black and white with a lot of flicker, phosphor persistence notwithstanding.

If you simply average the even and odd fields, you will be left with the completely incorrect result of 50% gray and zero change between image frames.

You seem to be under the misconception that two consecutive fields contain image from the same moment in time. This is not necessarily true with proper interlaced video.