This is a more complicated question than you may realize, and the answer can depend on several variables. You can read more at harmony+cross , but I’ll take a stab here.
Training methods are like OS’s for horses. Some methods (German Dressage) train the horse to push into the reins with their lower jaw intentionally – which from the rider’s perspective is effectively “pulling”. This notion of appui requires heavy contact, and the horse becomes used to leaning on this contact for balance.
Other methods (Baucherist Dressage, Doma Vaquera, Californio Vaquero) train the horse to operate on very light contact – e.g., the weight of the reins. As a novice, you would likely offend them with “pulling” yourself – to which they would initially respond by “giving”, but, finding no relief, they will eventually pull back.
Poor Training and Incomplete Training
Most likely, you are suffering through what most novices experience: early lessons on a lesson horse who is generally calm – but also either poorly trained, or who has developed numerous bad habits as a result of many student riders.
In the latter case, he is “pulling” because it provides a few seconds of relief against the bars of his mouth (lower jaw). Each time he pulls, it creates an instance of slack in the reins until you take the reins back in. Most novices (and too many not-so-novices) instinctively pull back again – in a confused attempt to “have the last word” (which repeats the cycle).
Ultimately, pulling results from one of two basic things:
1. Seeking physical relief from pain or discomfort (his mouth hurts due to injury, or your contact is too firm, or your contact is jerky, etc.)
2. Seeking psychological relief from the confines of the aids (e.g., he wants to look at other horses to your left, but he can’t – because your contact is physically pointing his head straight – so he endeavors to break contact to sneak a peek).
Correcting and Mitigating Horses Who Pull
The “Fixed” Hand
Revisit the fidelity of your hands. Focus on keeping your hand “fixed”, such that he rather “hits a wall” when he suddenly pulls – yet finds instant relief when he gives. Do not “pull” back – focus on keeping your hand where you had it to begin with. If your hand recoils toward you when he gives, you were pulling.
Lift, Don’t Pull
If he is setting his jaw against you and grasping the bit with his mouth to pull it away from you (and pulling so hard you can’t fix your hand), don’t pull back, instead and lift the reins – as if doing a bicep curl.
Lifting puts the action of the bit (presuming you’re using a snaffle) against the corners of his lips (which are helpless), instead of his bars. If you do this, he can no longer pull effectively. He can only lift his head and neck, which he will grow tired from doing very quickly.
Do this consistently, and he will teach himself that pulling creates more work than not pulling within 3 – 5 rides.