Nowadays, some people believe using public transportation is better for the environment than using private vehicles, whereas others hold the opposite opinion.

You need a conjunction to connect the two sentences

Personally, I agree with this viewpointe former for several reasons.

“The former” and “the latter” are really good words to know! “The former” is the first thing in a list of two things, and “the latter” is the second thing!

For example, private vehicles consume gasoline orand oil, which costs a lot of money, and your vehicle may also break down.

Cars need both gasoline and oil, so using “and” feels more intuitive!

Nowadays, some people believe using public transportation is better for the environment than using private vehicles, while others hold the opposite view.

You need to specify which opposite that people hold here. Since this is a contrasting statement it's better in writing to use a contrasting word like while. In spoken language you could get away with omitting it, but in that case you'd use tone or body language to emphasize the contrast

Private vehicles can cause many accidents, and traffic jams, which cause harm to the environment.

The oxford comma (comma after the last item in the list, before and - https://en.wikipedia.org/wiki/Serial_comma) is a stylistic choice, but even if you do use it, it's only for lists of 3 or more items. It's not used in lists of two items.

Nowadays, some people believe using public transportation is better for the environment than using private vehicles, others holdthink the opposite.

“Hold” isn’t used in that way.

Private vehicles can cause many accidents, and traffic jams, which cause harm to the environment.