There are two issues here; defining "progress" and equating evolution with it. I'll take the second one first.
When we "equate evolution with progress" we are typically making specific claims (sometimes without thinking about it). We mean that progress is an important priority of evolution or even its goal. We mean that evolution always leads to progress. And when we say "don't equate evolution with progress" we're saying that neither of those things is implied in the Theory of Evolution, and in fact, there isn't much evidence for either.
Humans are more advanced than dogs (again, skipping the question of defining "progress" for now), but humans and dogs aren't the only organisms around. E.coli is as much the outcome of 4 billion years of evolution as we are, yet we didn't "progress" in the same way at all.
One way of looking at it is thinking of diffusion. When I release a dot of dye into the water, it expands outward. Is there a specific force pushing it outward? Are any of the molecules trying to go outward? No, and no; all the molecules are moving randomly, and it is statistics that make it so their overall movement is outward; there simply is more space to move outside of the dot than inside.
And if I put that dye on the right edge of a water container, it would expand leftward. Again, is there a leftward force? Do all the molecules want to go left? No, and no: all the molecules are moving randomly, they just can't go further right than they already are, so for a molecule by the edge any random movement right keeps them where they are and any random movement left takes them left. And the overall average of the molecule's positions will move leftward, even though no specific molecule has a leftward bent (if they did we might expect molecules to disappear from the right edge, and in a diffusion situation they don't). Moreover, if we took the leftmost molecule at a certain point and looked at its trajectory over time, it would sure look like it's deliberately moving leftward... But that deliberateness would be an illusion; out of trillions of molecules moving randomly the odds are good that one of them would have made only or mostly leftward movements, and obviously that's the kind of molecule that would end up being leftmost in the first place. That doesn't mean it is being pushed left, or that its next movement will be leftward.
So applied to evolution, for almost all measures of "progress" we can come up with - size, intelligence, behavioral complexity, structural complexity, whatever - if evolution was pushing any lineage randomly along those variables we would still expect the maximum and even average size/intelligence/complexity to increase over time, because it would be very hard for life to become smaller, dumber or simpler than E.coli (harder but not impossible ! And we see examples of such trajectories, in parasites especially).
Now, you will tell me, evolution isn't random! Through natural selection, it leads to adaptation. True; it leads to adaptation to the environment. Change the environment, you change the direction that evolution will "push" a given lineage. And in the case of things like complexity or intelligence (the usual markers for "progress" in evolution), those traits can be adaptive or not depending on the environment; complexity allows more variety in responding to the environment, intelligence allows more productive interactions with said environment, but both have a cost, in risks of errors, in energy consumption, and so on. And so while you might say this lineage over this time period (in this environment) shows a definite trend towards complexity or intelligence (or gaining flight, or losing sight...), it is impossible to say the same of Evolution as a whole.
One point of evidence that the increase in maximum "progress level" is the result of diffusion and not a specific progress-ward force, is that as the right side of the container that still contained dye, the biosphere still contains tons of (a majority of in fact!) "un-progressed" organisms. This would not be true if Evolution as a whole were pushing toward progress. (in fact, you might note that I am not quite correct here! In a naturalistic view of abiogenesis, living things (or not-technically-living ancestors to living things) must have existed that were themselves outcomes of evolution but were incredibly simple compared to today's amazing bacteria, and those could be thought to be the lower bound in complexity, and Evolution did move life as a whole away from it! So we could argue that Evolution does move towards a minimal level of "progress" (the amount sufficient to compete against a bacterium). It's just that we reached that level over 3 billion years ago).
And to get back to the first point about defining "progress", once you dig down into what that means it can become all the clearer that evolution doesn't push one way or another. Bacteria have more metabolic diversity than Eukaryotes could hope for. Humans are more intelligent than dogs but worse at smelling. It can be argued that from a Müller's Ratchet perspective, "complexity" in Eukaryotes is pretty much constant, and any progress in one domain is the result of tradeoffs in another domain. This doesn't mean humans aren't more "advanced" than dogs, but it does demonstrate you need to be more specific about what "advanced" means for that to be true.