It seems that Toritoribe-san's explanation is efficient, so that the following might be unnecessary, but please let me add some. I hope this doesn't make you more confused.
The basic usage of もっとも is to supplement a partial objection...
I tried to tell above to Davide92-san but maybe failed because of my poor skill.
I'd like to explain step-by-step. Suppose that I have two opinions when someone asks me what I think about something:
- It does not count much.
- It may be true.
These are rendered to Japanse as
- 大したことではない。
- 正しいだろう。
To make sense, I need connect them. Let me assume the former is a sub-statement and the latter is main. Then,
(1) それは大したことではないが、正しいだろう。
(Although it does not count much, it may be true.)
This is the example Toritoribe-san wrote. (1) has a different nuance from
(2) それは正しいだろうが、大したことではない。
(Although it may be true, it does not count much.)
because in this case it sounds like 大したことではない is main.
In an actual conversation, of course there is a situation I say the main statement at first and then I want to add something negative as a supplement after:
(3) それは正しいだろう。大したことではないが。
(It may be true. It does not count much, though.)
This is just inversion of (1) as Toritoribe-san mentioned and makes sense enough. (This looks like (2) but the position of conjunction が is different.)
Now, if I say もっとも/と言っても/ただ/etc. after the main statement, the listener becomes ready for a negative supplement following.
(4) それは正しいだろう。もっとも、大したことではないが。
This works well even if I don't say が as I mentioned.
It may be possible to render (4) to English as written in Davide92-san's textbook:
It may be true. However, it does not count much.
in the sense that this expresses that right after the main sentence we notice a negative sentence follows.