I think our problem here is that when we say it in English, our word order is ambiguous. The 'official' answer wanted 'I also etc ...' to show that the 'also' goes with 'I' and not with 'boots'. I wouldn't worry too much about being marked wrong on this. We just need to remember that the word order in Italian will give us the true meaning.
"I also have a pair of red boots" is equally ambiguous in English. If the Italian really means that I, in addition to somebody else, have red boots (and not I have a pair of red boots as well as some other thing), the only way to express that unambiguously in English would be "I too have a pair of red boots."
I just added "I also have..." to the system. "Also I have..." to me doesn't correspond to the Italian, which means, "I, in addition to other people, have..." "Pure" attaches itself to the thing it follows, "io" in this case, so it's io + something/someone else. "Also I have..." implies more, "In addition to what I was saying before, I have...," which is not the meaning of the Italian.
Five questions down from this, Duolingo asks us to translate the English "They also live here." The answer I gave, "Pure loro vivono qui," was accepted. Yet translating in the opposite direction, it does not accept "I also have a pair of red boots" as a translation for "Pure io ho un paio di stivali rossi." Instead it corrects that translation with "I too have a pair of red boots", i.e., "I also..." is incorrect. It appears pretty clear that the logic underlying these two translations is inconsistently applied.
This is what I meant, with my comment I add earlier with another translation given by Duolingo. This is really not a right sentence: "I too have a pair of red boots" ??? You can say" I also have a pair of red boots", or I have a pair of red boots too!" But the translation of Duolingo sounds just wrong!
I'm not sure I believe that the Italian really means "I too have red boots" rather than "I have red boots as well as something else," but those who say it does may know Italian better than I do. So if you want to say "I have red boots as well [as something else]," in Italian, how do you do that?
Four years on and still no change, I see. No comments from a moderator. And while I'm here, and although it's good practising the Italian usage anyway, it's pretty clear that the architects of this skill did not know the difference between English adverbs, prepositions and conjunctions.
There is no excuse for this nebulous translation not being explained. It would seem that an uncertainty unanswered over four years indicates a significant problem with the system or possibly the people who are responsible. I am grateful for a free system. However, if the goal of Duoling is to teach us English, then this uncertainty must be explained!