There are no hard and fast rules about napping, particularly about when your toddler should drop their nap. And what children do with their naps in the UK is very different to what children do in Mediterranean countries, where they tend to keep their them awake much later in the evening and therefor keep a long lunchtime siesta right through to adulthood! #jealous
So back to the chilly UK, with our long cold winter nights and short-lived summers!
You may think that once your 2 year old starts fighting their lunchtime nap, they are ready to give it up.
You're probably misunderstanding your toddler's sleep needs and body-clock. They are most likely telling you that they are not ready to go for their nap at the time you've been putting them down, because the older they get, the longer they can stay awake. This means that you probably need to start their nap later and you may need to start capping it to ensure they are awake long enough to be tired at bedtime.
When babies are born, they can only stay awake for a few minutes. This quickly increases to half an hour and then an hour and a half within a few months. The amount of time they can stay awake gradually increases by around 15 minutes every 4 to 6 weeks, so that by the time they are around 16 months, they can usually stay awake for around 5 hours. This is the time that they usually start having "the long lunchtime nap", or "consolidating their naps" as is the popular term at the moment.
If you allow your toddler to lead you a little, you will find that they start showing their tired signs later and later in the day. They may well start to pickle about when you put them to bed for a nap, so you might find that as they get older, they will take more of a powernap in the buggy or car. This is ABSOLUTELY FINE and it shouldn't affect their night sleep.
So really, most children should stop napping between 3 and 4 years old. Some will stop at 2.5 years but this rare and what they probably need is a nap every 2-3 days before stopping completely.
Stopping your little one's naps too early will cause over-tiredness which will affect their behaviour and can affect bedtime.
All children a different, and what works for one may not work for another, but here's a bit of loose guidance.