Increasing entropy does not make everything equal, just indistinguishable.

Imagine a black and white tv. It has some large number of pixels, each of which can be either on (white) or off (black). Imagine that 50% of the pixels are on, and 50% are off. The most "ordered" way to arrange these black and white pixels is into two halves: one grouping of white and one grouping of black. There are many different ways that this could be, but there are so many more ways that it could be more jumbled.

For a tv with 1366x768 pixels, there are 2^{1049088} possible images. Most of them would look like "static" or "white noise." If a tv were to cycle through these different possible images, never repeating one, it would essentially look like the image is not changing except for the extremely rare instances in which the pixels form some arrangement we see as "ordered." It would then, almost certainly, change to another image that is totally "disordered." This has nothing to do with anything other than statistical probabilities.

Randomly cycling through the different possibilities is not a perfect analogy to the real world, in which the past and present states play a role in determining the next state. But there are randomizing forces (not Newtonian forces), and as the state of the universe evolves (not Darwinian evolution), it approaches this state of homogeneous disorder.

You can also think about flipping a coin 1000 times. It is possible to get 500 heads and 500 tails (with a fair coin), but it is more likely that it would be 501 of one and 499 of the other. Even if it did come out exactly evenly, it is highly unlikely that one would flip 500 heads and then 500 tails, or that it would alternate HTHTHTHTHT.... or that there would be any sort of discernible pattern. It is no more likely to flip HHTHTTHTHTT... than it is to flip any other ordering, we just wouldn't recognize that outcome as "special" in any way, just like HTHTTTHTHHHTT... These last two cases are not identical, but we see them as having similar levels of disorder.