While I certainly agree marine plastic pollution is a big problem, I prefer using those PET-bottles that can be bought pre-filled with water in the shop, for different reasons:

• Those bottles are approved to be used for the purpose of containing water for a longer time, and they don't give any taste to the water. They also don't leak. Buy a random empty water bottle in the shop, and there is no guarantee that it will be suitable for the purpose of carrying drinking water. Many of them do leech plastic taste.
• They can be reused over and over and over again.
• They are transparent, this is a nice feature for a water bottle. One can see that there is clean water in the bottle.
• Plastic bottles can be notoriously difficult to wash properly. They don't like high temperatures, and many of the empty bottles one can buy in the shop is with complicated lids or straws. Every now and then a water bottle needs a proper cleaning because someone used it for other purposes than water, or due to a biofilm buildup.
• Perhaps the bottle will be thrown rather than washed in the end. At least with my PET-bottle there exists good systems for recycling and the production cost of the bottle is as low as it can be. There is even a deposit on the bottle, increasing the possibility that it will be picked up and recycled should it get lost.

(Giving myself a modest upvote for better visibility)