The word "tradition" comes from the Latin traditio, the act of handing over (and so is etymologically related to "treason," a handing over in the sense of betrayal). In a general sense, a tradition is some pattern of behavior that is handed over from one generation to the next.
I've put together a state transition model of how this handing over occurs:
According to the model, each generation (be it an individual or a culture) has two kinds of behavioral patterns: "living traditions," which are received from the previous generation; and "personal patterns," which have a source other than the previous generation. A personal pattern can be created by the generation, reclaimed from an ancestral generation, or imported from an unrelated source.
Each living tradition is either handed on by the generation, in which case it becomes part of the cultural patrimony, or it is not, in which case it becomes a dead tradition. Personal patterns that are handed on also join the patrimony (and if a personal pattern isn't handed on, it just quietly disappears).
Each element of the patrimony is either accepted, in which case it becomes or continues as part of the living tradition, or rejected, in which case it joins the other dead traditions.
What's particularly significant about this diagram, in terms of how people relate to traditions that aren't handed down to them, is how dynamic it is. Tradition is often represented as an ossified system, from patrimony to living tradition and back. But a little thought shows that a lot more can be going on, even in relatively static cultures, and the diagram doesn't even represent the way a living tradition can evolve across generations or be adapted or understood by a particular part of a particular generation.
Creating personal patterns, then, is an inherent aspect of tradition, and shouldn't be regarded as unique to our modern, deracinated culture. Nor, for that matter, should our modern, deracinated culture be seen as altogether traditionless.