The effectiveness and protective time span of the Corona vaccines is not yet assured. Additionally, there are issues with ethic aspects and privacy. Now, even the WHO states that it rejects this idea.
Highest ethical value have the rights to the integrity of the person and to equality between people, vaccinated or not, which are part of the EU Charter. These are at risk due to the vaccination being an option to get back single fundamental rights at least for an unknown period of time. Free decision about vaccination is being manipulated like this and kind of discrimination is being established.
As the vaccination certificate shall be digital, there is in general a possibility of theft of personal medical data. Additionally, not only service providers like travel agencies get your vaccination status but also indirectly e.g. employers, in case employees are not allowed to travel abroad by plane
sources:
https://www.tagesschau.de/ausland/corona-impfpaesse-who-101.html
https://www.europarl.europa.eu/charter/pdf/text_en.pdf