Perhaps it's the phrasing - a 'pull' implies a directing (teleological?) influence from ahead, which only makes sense in terms of a goal. Even a 'push' has teleological overtones.
That's reasonable (though arguable) as a probabilistic statement, but not as an absolute.
It's a question of the particular context and relative advantage. For example, at the beginnings of evolution, when the first replicators had appeared, they were the simplest arrangements that could reproduce themselves with some random variation. Any variants that were simpler just couldn't reproduce. In this situation there are only two options for continuing to reproduce - stay as simple as possible or become more complex. Random variants that were more complex and could still reproduce would continue on. So in this situation it's almost inevitable that complexity will increase, even though the variation is entirely random.
At some point, complexity alone will become a disadvantage, e.g. slowing down reproduction, requiring more resources, and being more fragile and unreliable. At this point complexity will only increase if it provides some advantage that outweighs the disadvantages, for example, being able to make use of (eat) the teeming numbers of simpler replicators; and so-on.
The long-term result tends towards a pyramid of increasing complexity with vast numbers of simple organisms, with decreasing numbers of organisms as the complexity increases.
But complexity will only increase if it provides some advantage for survival and reproduction. Many complex organisms have evolved to become simpler as their environment changed and their previous level of complexity was no longer an advantage.
So there's no guarantee that complexity will increase, there's no drive or 'pull' towards complexity. If more complexity is possible and it provides an advantage, then it may increase, but unless it provides an advantage it won't.
Consciousness is a feature of the most complex life on Earth, and humans appear to have the most sophisticated form of consciousness; but it won't 'increase' by evolutionary means unless there's some selective advantage - and it's not even entirely clear precisely what we mean by consciousness, and what advantage it provides (there are some ideas), never mind what 'increasing' it means, and whether or how that would be a selective advantage.
It's possible that we could use technology to enhance consciousness in some way - some people say we already do that with devices that provide information, memory extension, and unbiquitous communications; but that's using a very broad definition of 'consciousness'.