I have heard this said in a disparaging way, as if it is foolish to aspire to goals beyond one's current limitations, or, put another way, as if one should not aspire to rise above one's station in life. According to an article in The Telegraph (U.K.; 2004), Britain's Prince Charles apparently claimed that "the modern education system went against natural selection and wrongly encouraged people to think they could rise 'above their station.'"
Maintaining the status quo is a pretty sweet deal for those who sit comfortably atop the class hierarchy, but it's not a particularly good deal for everyone else. It also goes against democratic or meritocratic ideals that many societies (including Britain's) espouse, so, no offence to the prince, but I would suggest that aspiring to rise above one's current station in life is natural, and should be encouraged.
Another Englishman, the poet and playwright Robert Browning (1812-1889) perhaps felt similarly when he wrote, "a man's reach should exceed his grasp” (line 97, Andrea del Sarto; 1855) in a remarkably long-winded dramatic monologue about a Florentine renaissance artist whose technique was said to be flawless, but who, according to Vasari, "lacked ambition and that divine fire of inspiration which animated the works of his more famous contemporaries, like Leonardo, Michelangelo, and Raphael." (Wikipedia)
Self-portrait of Andrea del Sarto (1486-1530)
His grasp apparently exceeded his reach; this may be why you have not heard of him.
David, by Michelangelo (1475-1564)
Sculptor, painter, architect, poet, and engineer;
Michelangelo's reach and grasp were huge. Like David's hands.
So, to summarize, Andrea del Sarto was a gifted painter with flawless technique, at least according to Vasari (and to be fair, not everyone agrees with his assessment), but history has not accorded him the exalted status of his renaissance contemporaries such as Michelangelo, perhaps because del Sarto lacked the desire to grasp the unattainable, whereas Michelangelo, like all great artists, had this desire in spades, as well as the technique to make it attainable.
Which brings us to composition.
If you have spent years learning to sing or play an instrument, you probably have a pretty good sense of what great music sounds like. You may also have an opinion of what bad music sounds like; the ability to make these kinds of judgement calls is something we all have, and it is called discernment. Not everyone agrees with our opinions regarding the relative merits of different artistic creations, but the point is that we make these judgements frequently.
One of the potential frustrations for university-age composition students is that, at the beginning of our composition studies, there is often a significant gap between the quality of the music we perform and study, and the quality of the music we write. This is to be expected, of course — the music we perform and study is often written by some of the greatest composers that ever lived, whereas music students are often relative novices and just learning the craft of composition — but it can be frustrating nonetheless.
I will call this the Skill-Taste Disparity. We have developed a sense of artistic taste that allows us to recognize great music when we encounter it, but our compositional skills are not yet sufficiently developed to allow us to create great music.
One solution would be to lower your expectations; if you don't expect to write high-quality music, then you probably won't be disappointed if your compositions are mediocre!
However, I don't suggest you do that…
Instead, I will reference Ralph Waldo Emerson — "Nothing great was ever achieved without enthusiasm" — and suggest that you approach all your compositional work with enthusiasm and intelligence, but understand that it takes time and dedication to eliminate any disparity that may exist between your musical taste and compositional skills.
Lowering your expectations may reduce your frustration levels, but I suggest that reaching beyond your current grasp is essential in order to become an excellent composer, and I encourage any aspiring composer to do this with enthusiasm!
Sure, there is a cost to this — I have done many things in life with tremendous enthusiasm, only to be figuratively have the wind taken out of my sails (or, to use a more visceral metaphor, to be kicked in the head by a mule with remarkably-powerful hind quarters) on numerous painful and doubt-ridden occasions (before the premiere: "This is going to be GREAT!!!" After the premiere: "OUCH! That SUCKED!!! Why did I ever think I could be a competent composer?) — but I don't know how to approach it any differently.
And I truly believe that if you stick with it, you will write very good, perhaps even great, music.