Oil is a limited resource that can be used for way more important things than disposable water bottles, such as medical supplies (syringes, IV bags, etc) and durable plastics components. Plastics themselves are a great resource that should not be wasted, not least because of the amount of energy and water it takes to produce them.

Most plastic bottles are burnt, so they do contribute to climate change; the small percentage of bottles that actually are recycled cannot be turned into new bottles --- plastics are always downcycled; recycled plastics are sometimes mixed in with virgin plastic pellets, but it's usually a relatively small amount of the total.

(I'm setting up an educational project for school classes on the topic of plastic recycling and renewable energy.)