So, recently, I learnt that T4 and T3 are both released into circulation but only T3 is the active form. Why then, do we make T4 in the first place? I read that T4 has a higher half-life, which might be the reason. Also, my professor said that it might be because thyroid peroxidase is not specific enough to control if it adds one Iodine or two. So, what is the actual reason?
It sounds like what you read and what your professor mentioned are different types of causation.
T4 is the primary form produced by the thyroid; T3 is metabolized from T4 in other tissues and more strongly activates thyroid hormone receptors. Metabolism from T4 to T3 then allows tissues to have control over how much active thyroid hormone there is - multiple levels of control are very common to hormones, and other signaling pathways as well.