So, I'm going to attempt to answer this question by framing it a little differently: Harrison wasn't a "bad" President, but he was an inconsequential President who had little impact on American history, largely in part because of his short tenure. Harrison's failure to do anything significant is part of the reason he's held in such low regard. The fact that it's not at all his fault isn't relevant because it doesn't change the fact that his Presidency had little impact on the course of the "Ship of State", if you will.
Let's use an aggregate ranking of the last 18 surveys of Presidential historians (from Schlesinger 1948 to CSPAN 2017) as a guideline for providing a concrete numerical guidepost for various Presidents: Harrison ranks 37th out of a possible 43 (Trump hasn't been ranked yet and Cleveland takes up 2 spots). Seems terrible, right? But let's take a closer look at how Presidential tenures are ranked relative to their time in office (again, out of a possible 43):
< 4 YEARS IN OFFICE
| Time in Office | President | Aggregate Ranking |
|---|---|---|
| 31 Days | W. Harrison | 37 |
| 6 Months | Taylor | 35 |
| 6 Months | Garfield | 29 |
| 2.5 Years | Harding | 43 |
| 2.8 Years | Kennedy | 10 |
| 3.4 Years | Ford | 26 |
| 3.5 Years | Arthur | 28 |
| 3.6 Years | Fillmore | 39 |
| 3.9 Years | Tyler | 38 |
| 3.9 Years | A. Johnson | 41 |
AVERAGE RANKING: 39.1
JFK is the clear standout here. He enjoyed astonishingly high approval ratings, was the centerpiece of one of America's most venerated political dynasties, and was cut down in his prime. Chances are, you remember JFK and Ford because they were alive recently... but the rest are either inconsequential or actually did damage to the country in some major way.
= 4 YEARS IN OFFICE
| Time in Office | President | Aggregate Ranking |
|---|---|---|
| 4 Years | Adams Sr. | 13 |
| 4 Years | Adams Jr. | 21 |
| 4 Years | Van Buren | 24 |
| 4 Years | Polk | 11 |
| 4 Years | Pierce | 40 |
| 4 Years | Buchanan | 42 |
| 4 Years | Grant | 36 |
| 4 Years | Hayes | 25 |
| 4 Years | B. Harrison | 30 |
| 4 Years | Taft | 23 |
| 4 Years | Hoover | 33 |
| 4 Years | Carter | 27 |
| 4 Years | Bush Sr. | 22 |
AVERAGE RANKING: 26.7
4 years is plenty of time to accomplish some sort of long term policy plan. By and large, we see mediocre and above average presidents in this group. Major exceptions include the two Presidents whose terms saw our descent into civil war.
4.1-7.9 YEARS IN OFFICE
| Time in Office | President | Aggregate Ranking |
|---|---|---|
| 4.1 Years | Lincoln | 1 |
| 4.5 Years | McKinley | 19 |
| 5.2 Years | L. Johnson | 12 |
| 5.5 Years | Coolidge | 31 |
| 5.6 Years | Nixon | 32 |
| 7.5 Years | T. Roosevelt | 4 |
| 7.8 Years | Truman | 6 |
| 7.9 Years | Washington | 3 |
AVERAGE RANKING 13.5 (15.3 without Lincoln)
Now we're starting to explore those Presidents whose performance not only merited re-election, but also spanned more than 4 years. We're kind of all over the map, here, as we have both Presidents who left office early (assassination or resignation) and entered office late (as in the death of their predecessors, in Nixon's case resignation, or in Washington's case, some awkwardness with regards to deciding the beginning of the Presidential term), but the common thread is that they all had a pretty significant amount of time to enact their domestic policy agendas. Lincoln, as the savior of the Union, tilts this number a little bit... but in my mind, I still see this inflated number as (at least in part) the manifestation of Shakespeare's claim that "Some are born great, some achieve greatness, and some have greatness thrust upon them."
8 YEARS IN OFFICE
| Time in Office | President | Aggregate Ranking |
|---|---|---|
| 8 Years | Jefferson | 5 |
| 8 Years | Madison | 14 |
| 8 Years | Monroe | 15 (tie) |
| 8 Years | Jackson | 9 |
| 8 Years | Cleveland | 18 |
| 8 Years | Wilson | 7 |
| 8 Years | Eisenhower | 8 |
| 8 Years | Reagan | 17 |
| 8 Years | Bush Jr. | 34 |
| 8 Years | Clinton | 20 |
| 8 Years | Obama | 15 (tie) |
AVERAGE RANKING: 14.7 (12.8 without G.W. Bush)
Other than George W. Bush, these are all Presidents whom historians rank as above average with regards to their effectiveness and ability to positively impact foreign and domestic policy.
> 8 YEARS IN OFFICE
| Time in Office | President | Aggregate Ranking |
|---|---|---|
| 12.2 Years | F. D. Roosevelt | 2 |
AVERAGE RANKING: 2
Now, I know what you're thinking: "This is a numerical anomaly, and doesn't merit it's own category. It's an outlier - who gives a fuck?" Now.... all of this is true. The reason I included FDR as a separate category, however, is because much of what made his Presidency highly consequential is because of the sheer length of time he spent in office. The New Deal took much of the 1930's to muscle through the gears of the American political system. FDR made huge strides with his Democratic allies in congress... but many of them faced hurdles when challenged in SCOTUS. In fact, FDR's first term was a disaster in this regard, and throughout the early years of his Presidency, FDR's New Deal legislation was repeatedly cock-blocked by the judiciary. How did he overcome this? Simple: He kept getting re-elected and he started appointing New Deal-friendly Justices to the Supreme Court. In all, he appointed a grand total of 8 Associate Justices and 1 Chief Justice (also: his VP, Truman, appointed 3 Associate Justices and 1 Chief Justice).
It's true that FDR led the nation boldly through WWII, but remember that his second term (which, at that time, was only customary) expired prior to Pearl Harbor. From the depths of the Great Depression (in 1933) to the manufacturing boom at the end of WWII spanned over 12 years: Far more than any other Presidency.
TL;DR: Harrison got screwed in that he had a short tenure. American Presidents are judged on their lasting impact on the nation, and because of our complex system of checks and balances, it takes time to enact change on a national scale