Let me explain why. By definition, destiny is "a predetermined course of events often held to be an irresistible power or agency." (Merriam-Webster)

Who predetermined the events? You did.
You, as a soul, planned various events before you came into this lifetime.

However, to arrive at such events, you need to follow your heart (not your brain) because your soul talks to you through your heart.

For example, I believe I was destined to become a healer to help particular group of people.

Before becoming a healer, there were various decisions that led me to this path - registering for healing workshop, getting certified as a healing teacher, starting to offer healing sessions and workshops, leaving a corporate job to be a full time healer, and so on.

In each of these decisions, I had good chances of NOT following my heart and making different decision, which would have made me stay being in a corporate job.

But I chose to follow my heart. Why? because I wanted to change my life.

It was scary though. I had good chance of NOT following my path because of fear and doubt.

These moments of decisions are what we call "divine timing" where we choose a new path or to stay in the same path. Diving timings will take place no matter what. However, whether you take the new path or not is totally up to your free will. Therefore, yes you can miss your destiny.