When it comes to synonyms for the phrase "be quarrelsome with", there are a number of options to choose from. Some possibilities might include "pick a fight with", "get into arguments with", "be contentious towards", "engage in verbal altercations with", or "dispute with". All of these phrases convey a similar sense of conflict or disagreement, suggesting that the person in question is someone who likes to argue or fight over even minor issues. Ultimately, the choice of synonym will depend on the specific context and tone of the sentence - some may be more appropriate for casual conversation, while others might be better suited for a more formal or serious setting.