One question about topological excitation in quantum many body system

You are abusing the brackets.

You should think about the whole thing without the brackets, which are merely a guide to the eye.

If you have a "ground state" configuration of alternating spin 1/2, $$ uparrowdownarrowuparrowdownarrowuparrowdownarrowuparrowdownarrowuparrowdownarrowuparrowdownarrow , $$ you can create a spin-1 excitation by flipping one spin. The resulting configuration will have three adjacent up spins, $$ uparrowdownarrowuparrowdownarrowcolor{red}{uparrowuparrowuparrow}downarrowuparrowdownarrowuparrowdownarrow . $$ Conversely, observe that the configuration which you describe has two places with only two adjacent spin ups, $$ uparrowdownarrowcolor{blue}{uparrowuparrow}downarrowuparrowdownarrowuparrowdownarrowcolor{blue}{uparrowuparrow}downarrowuparrowdownarrow . $$

Now if you look at this pattern, you can easily see that it is impossible to create it by flipping spins locally around where the two defects are located: To see this, just write the "ground state" configuration and the other one on otp of each other, $$ uparrowdownarrowuparrowdownarrowuparrowdownarrowuparrowdownarrowuparrowdownarrowuparrowdownarrowuparrowdownarrow\ uparrowdownarrowcolor{blue}{uparrowuparrow}downarrowuparrowdownarrowuparrowdownarrowcolor{blue}{uparrowuparrow}downarrowuparrowdownarrow $$ and you immediately see that all the spins in between the two defects differ (you can shift the vacuum by one site, then the same will be true for all spins outside the region between the defects).

To put it differently, the key to the "ground state" configuration is that the spins alternate up/down, while in your bracketing interpretation, only the pairs in the bracket have to differ, whereas in the second bracketing you write, adjacent spins in adjacent brackets can be rhe same. This is not a valid state.