I'm not sure Colangelo has ever specifically said why he wanted to buy the Jets, but I can provide some background on the move.

For those unaware, the Winnipeg Jets started in 1972 as an original member of the World Hockey Association (WHA). The WHA started as a competitor to the established NHL, and had a tumultuous 7 years before folding in 1979. Four WHA teams joined the NHL at that time, including the Jets.

Throughout the WHA's existence, the Jets were one of the top teams in the league, winning 3 of the 7 championships. They were also bolstered by the addition of Bobby Hull: a star player in the NHL, he famously signed with Winnipeg in 1972 for a 10 year, $1.75 million contract, which included a $1 million signing bonus (one of the largest contracts in sports at the time). The Jets were also one of the first North American teams to sign European players, which also helped them become good.

That all said, the NHL did not like the WHA, as it cost them a lot of money, namely in terms of player salaries. So when the 4 WHA teams joined the NHL in 1979, they were effectively punished: they had to pay a $6 million entry fee, and were only allowed to retain 3 players from their final WHA roster (teams had roughly 20 players at the time). The WHA teams predictably did not do so well in their first NHL season, and had some troubles over the next few years. Winnipeg in particular had one of the worst seasons in NHL history the following year, 1980-81, winning 9 of 80 games. They did slightly improve throughout the 1980s, but were in a division with fellow WHA refugee Edmonton Oilers, who became one of the dominant teams in the decade, and thus never really found success.

At the same time the sports landscape was starting to change. The salary explosion of the 1970s tapered off a bit in the 1980s, but blew up again as the 1990s started: in 1989 there was something like 3 NHL players making $1 million or more, while by 1996 (the year the Jets moved) the average salary was something around $850,000 (I can't find specific numbers at the moment). This was notable because starting in the 1990s, all salaries were paid in US dollars, which meant a team like Winnipeg earned revenue in Canadian dollars but paid their largest expense (salary) in US dollars. This was also a time when the Canadian dollar dropped sharply in value relative to the US, reaching lows of $0.70 (if not lower).

To accommodate for the new rise in salaries, sports teams began to build new arenas with modern amenities (namely luxury boxes): 12 arenas were opened between 1989 and 1996 (the NHL peaked at 26 teams in this era), and a further 17 since then (only 3 predate this era, and 2 of them have gone through complete retrofits).

Winnipeg's ownership tried to get a new arena built at this time, to replace their current arena, which was built in 1955 and had both a limited capacity and no luxury suites. However the Jets' ownership did not have the financial ability to build an arena themselves, and when they went to the various branches of government (municipal, provincial, federal), they were not given support (note: American governments are much more accommodating in this regard than Canada). Losing millions of dollars running the Jets, the team was effectively out of options in Winnipeg.

Now we get to the point of the team moving. As you noted, there was a plan to move them to Minneapolis-St. Paul, Minnesota. This was a city that had an NHL team, the Minnesota North Stars, from 1967 to 1993, before they moved to Dallas and became the Stars (this was again an arena issue: the North Stars played in the suburb of Bloomington, and the arena was old and ultimately demolished to become the parking lot for the Mall of America). A new arena was built in Minneapolis to house the NBA's Minnesota Timberwolves, but the deal ultimately fell apart (in 1997 the NHL awarded an expansion team to Minnesota, the Minnesota Wild, who began playing in 2000, though in a new arena built in St. Paul).

Enter Jerry Colangelo. He owned the Phoenix Suns of the NBA and the newly-formed Arizona Diamondbacks of MLB, and controlled the arena in Phoenix (I don't know if he actually owned it outright, but certainly had management rights). He partnered with two other Phoenix-area businessmen, Steve Gluckstern and Richard Burke, to buy the Jets and move them to Phoenix, where they were renamed the Phoenix Coyotes. However the team didn't make money, instead losing millions as player salaries continued to rise dramatically (culminating in a year-long lockout from 2004 to 2005; a salary cap was implemented after that, which remains and has had a major effect on things), and Colangelo sold his interest in 2001.

As to why Colangelo thought it was a good idea, like I said I don't know if he's specifically spoken on it (he very well could have though). But it would have fit with the larger trend of North American sports of the early to mid 1990s, the NHL in particular: the leagues were expanding, and following demographic trends of the US, which was growing in the south and in the west. This led to the idea of the NHL's "Sunbelt" expansion: from 1991 to 2000 the league added 9 teams and relocated 4, and 8 of those 13 were in southern or western markets (the NHL added an additional 2 teams in 2017 and 2021, with one more in the Sunbelt). Phoenix was also one of the fastest growing cities in the US, a pace it has kept up for decades, and thus had millions of potential customers for a hockey team. It should also be noted that Phoenix did have a history of hockey dating back to the 1960s, with various minor league teams, and one stint in the WHA even (all named the Roadrunners).

I will add a short post-script here, but keep it brief as it's within the 20-year rule, and because the saga isn't over yet: as noted Colangelo sold his interest in 2001, to a group led by Jerry Moyes and former NHL great Wayne Gretzky. This group moved the team to a Phoenix suburb, Glendale, in 2003 to a brand-new arena, built specifically for the Coyotes (the original Phoenix arena was built to NBA specifics, and thus had thousands of obstructed seats for hockey). This failed for several reasons, and the Great Recession also took a huge toll on things. The end result was Moyes declared bankruptcy in 2009, and tried to sell the team to Jim Balsillie, who wanted to move the team to Hamilton, Ontario. The NHL sued to prevent this, won, and blocked the sale, and took over ownership of the team. Several different ownership groups took over since then, they've all lost millions of dollars, and the current owner, Alex Meruelo, has had the lease in Glendale terminated as of this year, so the team will be playing at a 5,000 arena on the Arizona State University campus for the next few years while Meruelo tries to build a new arena in nearby Tempe. It's been a really convoluted, bizarre series of events since 2008, and the end is still not in sight.