McVeigh's second daughter Lolita-Luella was born last year and he was a key figure in the Swans' upset Grand Final win over Hawthorn.
One of the iconic images from that match was McVeigh holding Lolita-Luella to his chest on the MCG as the Swans celebrated the win.
"If anyone is questioning whether their kids should play footy after all that has gone on recently in the world of sport, I can only say the vast bulk of footballers and football people are quality individuals with values I admire," McVeigh said.
"What I've learned during the past two years is that in the hard times, your teammates are your brothers, your club's supporters are like family and your peers at other clubs are your friends.
"Football and its people envelop you, embrace you and help you stay strong."
Click here to read a transcript of McVeigh's full speech from the AFL Season Launch, or click on the video player above to watch McVeigh's speech from Monday night's Sydney Swans Guernsey Presentation
McVeigh spoke at Wednesday night's season launch in Melbourne, where AFL chief executive Andrew Demetriou also warned that the League could not have a win-at-all-costs attitude.
Last month, Essendon came under investigation for supplement use and two days later the Australian Crime Commission issued a landmark report about sport in this country.
"As we start this season, it would be naive of me to ignore the fact some people believe there is a shadow over sport in Australia," McVeigh said.
"I trust the authorities and senior administrators of all sports are doing whatever needs to be done.
"We live in a highly competitive environment and it's fine to challenge convention and push the boundaries, to try to be better.
"But in the end, I believe that hard work is the only secret and it will always prevail."
