This question or line of thought seems to be becoming relatively common even amongst some whom I know are otherwise sensible, so let's look at it clearly shall we?
1. Unvaccinated people are more likely to get the virus than vaccinated people.
This is clearly true, and can be understood by the common person when you remember that those who are vaccinated and get the virus are classified as having gotten a "breakthrough" infection. That means that, despite the additional protection offered by the vaccine, it's not a 100% preventive and so even vaccinated people can get the virus. However, it is obvious that two identical twins - one vaccinated, one not - who are exposed to the same circumstances will have the unvaccinated one more likely to get the virus. Therefore, statistically, you ARE more likely to have the virus if you're unvaccinated with all other factors unconsidered. This is the main reason for restrictions. If you're a vector, I don't want you wandering around near me. In addition, if you DO get the virus, the unvaccinated are more likely to get long-haul COVID, have a longer time with the virus before recovery and have more serious impacts from the virus. This makes them a burden on the healthcare system and families who have to care for them and a higher risk because they're actively transmitting the virus for a longer period of time after getting it than the vaccinated are by virtue of their being able to recover more quickly and completely.
2. Unvaccinated people are more likely to behave with less caution in terms of getting or transmitting the virus.
I would say that there are two camps of unvaccinated based on my observation. First are those who are genuinely concerned about the vaccine impacts on their personal health but who recognize that the virus is a serious health concern and take extra precautions (being especially careful about masking, avoiding crowds, maintaining social distancing etc.) knowing that they haven't got the vaccination to provide additional protection. Those people are not problematic because they're behaving in a way that protects themselves and others from what they recognize as a public health danger. With their behaviours and masking, they're not recklessly exposing others to the virus, although they're personally in more danger should they get infected despite their precautions.
The second camp are the real problem - the "I know better than the scientists" crowd, the "muh freedumbs", the "vaccine-shedding", the "micro-chipping", the "sheeple" and the "whatabouters"...it's been a revelation to me that this group extends far wider and deeper than previously believed and includes people who ARE scientists and health professionals. However, as one who grew up in a medical family, it's actually not that unusual for health professionals to eschew what they know to be sound medical advice in favour of doing what they want despite the impacts. In these cases, there are usually two main reasons underlying those choices: (1) Political belief, (2) Personal convenience/pleasure, (3) Fatalism, (4) Susceptibility to conspiracy theory, and (5) Mental illness. These people have politicized a public health issue and are not willing to either consider other people's rights as being as valid as their own, or are basically of the opinion "we're all gonna die one day and this place is going to hell in a handbasket anyway" or have become influenced by deliberately targeted and malevolent social media to act as the "sheeple" they so despise. In addition, because of the politicization of the issue, these people are also now gathering with other like-minded individuals to promote their point of view, and of course not taking the pre-cautions to prevent transmission of the disease so are higher in actual exposure to the virus. These people are a real and present danger to the public. They are the reason for the restrictions and why, suddenly, after a lifetime of getting vaccinated, there are all of these internet experts "DoInG thEIr ResEARch" to tell us all about the science and epidemiology they haven't previously given a thought to for their entire existence. But of course without the grounding to understand a whit of it.
The biggest problem is separating these two groups of unvaccinated people. Since there's no easy, obvious or scientific way to do so that is practical, unfortunately for the first group, they're going to have the restrictions imposed on the second group. Those restrictions are necessary to protect the rest of us who are complying with the public health mandates and practices.
TL;DR: You are statistically more likely to be a danger to someone else in terms of transmitting COVID-19 if you are unvaccinated because your likelihood of getting the virus is higher and you're more likely to transmit the virus due to your views that have lead you to not get the vaccination. This is not universal behaviour among the unvaccinated, but in order to manage the virus practically, this group has to be treated uniformly in order to protect the majority of the population and, especially, the vulnerable.