When you do something inattentively, your mind is only half there. You may be looking, writing, or nodding — but you are not really taking the person or the thing in. It tells you HOW an action was done, not what kind of person someone is for ever. A student can copy a sentence inattentively and change a letter without noticing; a driver can change lanes inattentively because a thought pulled them away. It does not have to mean they chose to be rude. Tiredness, worry, and trying to do two things at once all make this easy. The word is a little formal. Friends more often say you were not really listening, or you did it without paying attention. Teachers and writers like inattentively because it is neat and a bit serious. Though actually, people stretch it: even a kind “mm-hm” on the phone can be given inattentively if your eyes are on something else.