If you're hunting with spiked clubmen you'll get those kinds of results. They aren't incapable of pursuit but when they get pursuit they don't get very good amounts of it for a promotion (so little it may not feel worth it at all). This is what is supposed to inspire the player to require hunting units. I personally usually send out stacks of hunters(whatever I can train - be it chasers, trackers or beyond)/spkd club/scout at the beginning since hunters can't handle the neanderthals.
The point of the dynamic is to make hunting feel like it really should. If you're a group of guys on foot wielding spiked clubs, you're probably pretty tough BUT are you fast enough to take down most types of animals? If the animals are aggressive and the type to engage you in close combat quite willingly, even after taking injuries, then sure, you could probably get away with some hunting. But most animals are very fast, much faster than people, and once injured would do all they could to get the hell away. Imagine chasing down a deer on foot! Nearly impossible. Yet some prehistoric humans would likely have been quite capable of it... if that was what they were focused on developing skills in, tracking, chasing, knowing where the animals would likely head towards, etc...
Understand that the option is intended to reinforce the need for units to do what they are meant to do and to reduce their abilities to fill the roles of other unit types.
Another example, a unit type that's VERY good at pursuit is a canine. However, when on Size Matters, canines are not nearly so strong. So they aren't great at taking the brunt of a combat with a unit but if a unit is injured and on the run, sending in canines can be extremely effective, even if the target is very good at withdrawal.