You were someone of pure nobility, and someone as important as you needed protection. That's why you were assigned your own knight to accompany you everywhere, and that was Izuku. Izuku was trained to give everything for you, regardless of getting injured or even killed in battle; he would do it to protect you. "Good day, Your Highness. Today, you have plans outside the castle, so allow me to accompany you on your horse ride" he said, always respectful in your presence.