Do you have a similar problem with Missions that require you to play Summoner's Rift (e.g. "Kill a dragon." "Place a ward")?
Because if you're complaining about any Mission that's limited to specific game modes, then that's pretty reasonable. It's irritating to feel like you're forced "encouraged" to play a mode that you aren't interested in. However, if you're just complaining about non-SR Missions, such as these ARAM Missions, then that's very much unreasonable. If some Missions are going to cater to Rift, then it's only fair for other Missions to cater to other game modes.