There are a number of magic items in the DMG that set a stat to a certain number if it's not already higher than that number, like the Headband of Intellect, which sets your Intelligence score to 19 unless it was already 19 or higher. A lot of them set the stat to 19 specifically, which might be significant, but the Belts of [X] Giant Strength are 21, 23, 25, 27 and 29 for their respective giants.
There is almost no benefit provided by a score of 19 over a score of 18. (Or 21 over 20, and so on.) Why were these items designed to give an odd score?
Answers should be backed up with statements from the designers explaining their reasons for this odd (pun intended) choice.
The items set the ability score to an odd number so that there is still an incentive for characters to maximize their primary abilities by gaining class levels.
Imagine you're playing a Wizard, and you find out that a single item can bring your Intelligence up to the maximum of 20. You can spend your Ability Score Improvements on feats or increase other ability scores. Suddenly the only motivation you have to put points into Intelligence is to stay viable until you can acquire a Headband of Intellect. As for the various Belts of Giant Strength, it is possible for a Barbarian to get his Strength up to 24. Once you take that into account, by choosing 21 and 23 as the two initial power levels for the belts, the game's designers seem to be following the same pattern set by the Headband of Intellect and the other items. Set the score high, but not high enough to be optimal. The 5th Edition developers simply do not want you to be able to max out your most important ability with a magic item.
As for why a 19 as opposed to an 18, at least in the case of Strength a 1 point increase can provide a slight benefit in the form of carrying capacity. Also, Strength requirements for armor are odd scores (Chain Mail calls for 13 Strength, Splint and Plate both bring it up to 15). Unfortunately, beyond that, your question isn't really answerable as it calls for speculation into the human thought process. The only ones who really know for sure are the game's designers. Everything else is opinion. I have tweeted Jeremy Crawford regarding this question and will update my answer as soon as I receive a reply.