Note: I had the same question. Below are some of the points that a bit of Googling turned up. My comments in parens.
Some issues that some seem to have with it.
1. Some are concerned with the emotional effects on the surrogate. There are strong biological factors that make a mother get strongly attached to the child they carry, so giving it up immediately could be bad for them.
(tzs: I don't see how this is different from women who give up for adoption a newborn conceived the conventional waw, so this issue seems to me to be orthogonal to surrogacy)
2. Some say it promotes the commoditization of women's bodies, especially poor women. There is actually "surrogacy tourism", similar to "sex tourism", where people from wealthier western countries go to poor countries where there is a thriving trade in rental wombs. As with the women in those countries who serve the sex tourism trade, the women proving the wombs are often coerced into the business and are not getting the rewards.
3. Some say that there are already born children who need adoptive parents. People who cannot have children the conventional way should be adopting those children.
I saw a response to that argument, pointing out that a couple that waits until their careers are going well to try to produce children might try for quite a while to conceive before suspecting something is wrong, then might spend a few years trying various fertility treatments. By the time all of that fails, they can easily be too old to be allowed to adopt.
4. Recognition of surrogacy varies quite a bit around the world. Commercial surrogacy is legal in India. Altruistic surrogacy, but not commercial surrogacy, is legal in the UK and Australia. All forms of surrogacy are prohibited in France and Germany. In the US it depends on the state, some allowing commercial surrogacy and some prohibiting it [1].
This could lead to children with questionable legal status. If you had a couple from country X, a "no surrogacy" country, acquire a surrogate child in country Y, a "fully recognized commercial surrogacy" country, it might be possible to get a situation where there is no country that recognizes the child as one of its citizens.
(tzs: overall, from what I read, it seems no one has offered any good argument that surrogacy is inherently unethical, but there is a lot of potential for abuse, and a lot of areas it can touch that you could easily overlook such as interactions with things like citizenship. It seems to be one of those areas where you should regulate it from the start, rather than letting it develop commercially freely and then try to patch up any bad aspects you discover).
[1] https://www.creativefamilyconnections.com/us-surrogacy-law-m...