Without having sample pictures with EXIF attached, "we" (the internet community) can only make reasonable guesses at the problem.
As indicated by previous respondents, when shooting at or near wide open on fast lenses (f2.8 and wider), the depth of field can be surprisingly thin, especially when shooting from less than 10' from the subject with a medium telephoto. That can often be the cause of slighly-soft results.
Another common 'soft' error is incorrect focus point. Canons' AF system will typically choose the nearest 'subject' and focus on that. With thin DOF, even someones' shoulder angled toward the camera could become the focus point making the face soft. The key is to verify what the camera is 'locking in' on. And while on the subject of AF - AI-servo...absolutely, AI-servo. If it moves/breathes/flaps/waves in the breeze, AI-servo.
A too-slow shutter speed is the next potential culprit. For people as subjects, even if they are posed, 1/125 is about the slowest to reliably freeze their action...I've been surprised too many times thinking 1/60 was fast enough to stop motion. At 1/60th, expect a sharp head shot ratio of 1 in 4...or 5...or worse.
And, of course, camera instability can cause a slight blur. The general 'rule' for camera stability is 1/focal length or faster. That's generally true. But still, 1/125 or faster to freeze human subjects supercedes it in my mind, unless I'm shooting with my 135 and longer lenses. With IS, slight hand movement is corrected by the lens, but IS can't stop subject movement, unfortunately.
Lastly, the lens and camera might need MFA - Micro Focus Adjustment to get that last 'bit' of sharpness.
With my 5D3 and f2.8 and faster L glass, I routinely have to use ISO 6000 and faster to get decent results with no flash indoors. It's all about the exposure triangle and getting enough light to the sensor to get a decent exposure level.