When the city arborist makes a decision about a tree that you do not agree with, it is within your right to file an appeal. However, you should know the law before going into the hearing. It will be helpful to review the Tree Removal FAQ and the full Tree Protection Ordinance so that you fully understand what the law does and does not protect.
Many people try to argue their appeal based on emotion, personal fears, impact to their own property value, or beauty of the neighborhood -- the Tree Commission's decision cannot be based on any of these things. It is fine to describe the property's unique features to provide context, particularly if the site contains any champion trees or if tree removal will cause stormwater runoff to affect the adjacent properties, but make sure that the Tree Commission has specific sections of the tree ordinance that can be used to uphold your appeal. It is not the City Arborist's nor the Tree Commission's job to advocate on behalf of saving trees. Their responsibility is to enforce the Tree Ordinance as written. So, to the greatest extent possible, highlight the specific sections of the tree ordinance that the preliminary permit you are appealing does not comply with.
If you don't like the way the Tree Ordinance is written, then please join The Tree Next Door to advocate for changes to the tree ordinance. You cannot use the appeals process to re-write or re-interpret the law.