My Dad, who is a professor of history, always used to say that being a historian is like being a detective, piecing together many different sources of incomplete or false information from unreliable sources, assessing motivations for actions, and so on.

You may indeed be able to establish some facts with high confidence. Many others will be suppositions or just possibilities. Establishing "facts" though is not really the point (despite how history is taught in school).

You try to weave all these different things into a bigger narrative or picture. It is most definitely an act of interpretation, which itself is embedded in our current conceptions (some of which are invisible to us and which future historians may then riff on).

Saying that you don't like the subjectivist take on history means you think there is an objective history out there to be had which we could all agree on, but that does not exist.