Is "lonely" one of the top 4 adjectives you'd pick to describe fatherhood? top 25? Maybe if they've described the costs in terms of benefits (as you did) it would be more accurate; I think they might mean it CAN BE emotional, draining, (still not sure about lonely) AT TIMES. If I was betting on it I'd guess they came to this characterization while trying to come up with their call to action, (probably subconsciously). Nothing sinister just off the mark.
I think it depends on how you interpret lonely. I've always had a great support system in family and friends so I haven't been physically lonely. But feeling a sense of failure or that I'm dealing with a specific issue that no one around me understands does make me feel lonely or isolated. From other comments in the thread I got the impression that OP has done a lot of research that led them to use "lonely" as one of the main emotions worth mentioning in their pitch.
