Wildlife photography punishes slow decisions.
Your subject does not care that you were still deciding whether 1/500 was enough.
Shutter Speed Is About Movement
The correct shutter speed depends on what is moving and how fast it is moving.
A sitting bird and a bird taking off are completely different problems.
For relatively still wildlife, moderate shutter speeds can work. For running animals, flying birds or rapidly moving subjects, you need much faster shutter speeds.
The 180–600mm range I use makes this even more obvious. Long lenses magnify movement, including yours.
Faster Is Not Always Better
You can always increase shutter speed, but there is a cost.
Faster shutter speeds require more light, a wider aperture or higher ISO.
In poor light, freezing the subject may mean accepting noise.
That is often the correct trade.
A sharp photograph with some noise is usually more useful than a clean photograph with motion blur.
Watch the Subject, Not the Number
Do not memorize one shutter speed and use it for everything.
Look at the behavior.
Head movement, wing movement, running, jumping and flying all require different decisions.
What Actually Matters
Wildlife photography is a continuous exposure tradeoff.
You are balancing shutter speed, aperture and ISO while the subject is doing something unpredictable.
The goal is not the lowest possible ISO.
The goal is getting the photograph.