Reason they're out of the race: The bullpen
On the flip side, the bullpen has been an unmitigated disaster for the Cubs of late. Only three relievers who have pitched this year (not counting Tucker Barnhart) have ERAs that don't start with a four or higher. One of those relievers, Jeremiah Estrada, has some major red flags across his 8 2/3 innings in the majors too. For as disgusting as his stuff is, he's also walking 17.5% of the batters he faces with a hard-hit percentage of 69.1.
The rest of the bullpen is marked by failures to sign more reliable veterans and major steps back from once-reliable arms. Both Michael Fulmer and Brad Boxberger, the team's two bigger bullpen additions, have been unplayable with a 7.48 and 5.52 ERA respectively. Things have taken an especially disastrous turn for Keegan Thompson who came into the season as one of their biggest bullpen weapons. Across 21 1/3 innings, he had a walk rate north of 15%(!) which helped earn him a swift demotion to Triple-A where, unfortunately, he hasn't done any better.
It's hard to see how things turn around quickly without some drastic measures. Cubs president Jed Hoyer took the blame for the bullpen failings and hinted at more starters like Ryan Jensen, Luke Little, and Daniel Palencia being in play later this year as relievers, but it'll take a lot of arms turning it around or new relievers hitting in order to make this bullpen playable. As one final measure of their struggles, the arms who have thrown in relief this year have been worth a collective 1 fWAR which just won't cut it.