OK, I don't believe the Dad's original comment.
But...for most situations, being called up to varsity playoffs extends a player's season.
There are a couple of reasons why a player might want to not extend his HS season. One is to allow the player to take part in the practices for the next season's sport. An obvious example (which recently occurred at my son's school)-- sophomore basketball player is also a golfer. He was called up to varsity at the end of basketball season and missed the the initial practices/matches of the varsity golf team. Of course, he took part in the BB playoffs, but there was a downside for golf. Similarly, a kid who plays both baseball and football might prefer spring football practice to getting experience sitting in a varsity dugout.
Locally in California, a high school baseball player can't practice/play with an outside team during the season. If his travel team is already practicing, he may want to join that team. If the freshman player is baseball age 14, he may see the travel team as a better use of his time, because 14U tournaments run throughout the spring.
Having said all that, I'm hard pressed to believe that any player would turn down the opportunity to be part of a play-off run. At the two high schools I have sons at, turning it down isn't even allowed. Once you start a sport, you are supposed to see it through to the end of the season.