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Monasteries are wary about people inquiring because they can't hack it in the world. And because monasteries are businesses of a sort, they are concerned with what a middle-aged inquirer can bring to the table financially.
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That's a very broad statement; the reality depends on the specific order and monastery in question. To be sure monasteries are wary about all who inquire, thus the usual two-year neophyte period. Beyond that some will expect more from novices, other less, but there are many stories of broken people retreating to monastic life even today. Indeed many (within the Church) expound that as a key role of monasteries, providing a place for people to escape from the world. If you just want to live a Godly life, you can do that in society; monasteries are precisely the place you go to do so outside of it.
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A pithy saying in both the Catholic and Orthodox traditions is that people shouldn't consider monasticism if they want to run away from the world, but rather only if they want to run towards Christ. A significant part of the discernment process is weeding out the former.
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