The Chicago native played on the same DePaul team as future NBA star, Terry Cummings, and found himself in the national spotlight during his three years at the university. He averaged 24.0 points as a freshman in 1978–79, and led the Blue Demons to the NCAA Final Four. Over the next two seasons he scored 26.8 and 23.0 points per game, respectively, and was named College Player of the Year in 1980–81. A member of the 1980 U.S. Olympic basketball team, Aguirre left school after his junior year. The Dallas Mavericks selected him with the first overall pick in the 1981 NBA Draft.
Aguirre averaged 20 points per game over the course of his 13-year NBA career. He was selected as the first overall pick by the Dallas Mavericks in the 1981 NBA Draft and remained with the Mavericks until 1989.
In his first season Aguirre was limited to 51 games and averaged 18.7 points, second on the team to Jay Vincent (21.4 ppg). The Mavericks improved by 13 games in the win column and finished ahead of the Utah Jazz, but were still twenty games behind division-leading San Antonio Spurs.
Beginning with the 1982–83 season Aguirre reeled off six straight campaigns in which his average topped 22 points per game. In the first of those seasons he scored 24.4 points per contest, tops on the team and sixth in the league. The Mavericks continued their ascent, bettering their record to 38-44 to finish ahead of Utah and the Houston Rockets in the Midwest Division.
During the 1983–84. Aguirre averaged 29.5 points per game, second in the league to Dantley's 30.6 ppg. He finished the season with 2,330 total points.
Although Aguirre was the Mavericks’ main weapon, he was helped by the emergence of Rolando Blackman (22.4 ppg) and the contributions of role players Brad Davis and Pat Cummings. Dallas finished second in the Midwest at 43-39, and the team made its first playoff trip, beating the Seattle SuperSonics in the opening round before losing to the Los Angeles Lakers in the conference semifinals.
In each of the next two seasons the Mavericks posted identical 44-38 records. In 1984–85 they made a quick exit from the playoffs, bowing to the Portland Trail Blazers in the first round; in 1985–86 they defeated Utah and then took the Lakers to six games in the conference semifinals. Aguirre averaged 25.7 and 22.6 points for those seasons.
In 1986–87 and 1987–88 he made the All-Star Team and averaged 25.7 and 25.1 points, respectively, during the regular season. The Mavericks won more than 50 games each year. The 1987–88 edition of the franchise went 53-29, beat Houston and the Denver Nuggets in the first two rounds of the postseason, then extended the Lakers to seven games before losing in the Western Conference Finals. It was the longest postseason run in the Mavs’ eight-year history.
Both Mavericks single-season scoring records still stand. His 13,930 points as a Maverick rank third in the franchise's history, behind Rolando Blackman's 16,643 points and Dirk Nowitzki's 26,786 (updated June 14, 2014).
While Aguirre's time in Dallas was full of high-scoring efforts and playoff visits, the Mavericks were postseason underachievers (their only Western Conference Finals visit was the 1988 loss to the Lakers), and Aguirre had repeated conflicts with coach Dick Motta and players like Blackman, Derek Harper and James Donaldson. Then-team owner Donald Carter was a huge fan of Aguirre and hoped he would remain in Dallas for his entire career, but eventually conceded that the gulf between Aguirre and the team was unbridgeable. Midway through the 1988–89 season Aguirre was traded to the Detroit Pistons for Dantley, who was also one of the league’s top scorers, and a first round draft pick on February 15, 1989.
After Aguirre joined them, the Pistons became NBA champions in 1988-89 and then repeated as champions in 1989–90. Aguirre came off the bench for Dennis Rodman and averaged 14.1 points, fourth highest on the team. He showed he could blend into a successful team by taking fewer shots, playing hard on defense, and not complaining when Rodman's minutes increased greatly over time. In the 1990 playoffs, which culminated with a five-game Finals win over Portland, Aguirre averaged 11.0 points.
Aguirre played three more seasons with the Pistons in an increasingly limited role, due to both Rodman's play and his own age and injury issues. In 1993, the Pistons released Aguirre and after he cleared waivers the Los Angeles Clippers signed him for $150,000 for a partial campaign in 1993–94. Through the 1993–94 season Aguirre had accumulated 18,458 points for a career average of 20.0 points per game. He retired in 1994.
Aguirre, whose father was born in Mexico, at one point considered playing for team Mexico at the 1992 Olympics.