National sporting teams are not kicked out of league based on lack of performance so the Browns should not be kicked out of the NFL just because they have not won a game all season. It would be unfair to the Browns as well as the other teams the Browns play to kick them out of the NFL.
You can't just kick a team out. We would then still need to put another team back in so we have an even amount of teams so everyone has a game to play each week. Then that team will be in a rebuilding stage, playing just as bad as the Browns. Anyway when our favorite teams aren't playing good we always need a good team to beat up on to get our confidence back.
Lots of teams go through dry spells. The Chicago Cubs baseball team is a perfect example of that. It's fun for other teams to beat them, but most importantly, after time they will find a way to improve. They need to bring in new managers and give them time to implement their plans.
Although the Browns are on a long losing streak, they should not be kicked out of the NFL. Many NFL teams have, historically, performed very poorly; for example, both the Tampa Bay Buccaneers and the Detroit Lions have had seasons in which they lost every single game. But those teams improved drastically in subsequent seasons. Even if the Browns are performing poorly this year, this does not mean they will not have strong seasons in the future.
No, they should not be kicked out of the NFL because the Detroit Lions won zero games in a season not that long again. The Lions have since been a playoff team. The Browns need help but they have been in the league for a very long time and they have a good fanbase.