bad white opening?

Since I'm a pretty low-rated player, I usually play this opening and don't really play fancy openings.  I played this opening against this really good guy in my chess club.  I play it every time as white, and he tells me that it's a bad opening.  Is that true? 

Yup, 4...Nxe4 5. Nxe4 d5 6. Bd3 dxe4 7. Bxe4 Ne7.

No, it isn't. Perhaps your opponent is thinking of 4...Nxe4 which has been claimed good for Black. But after 4...Nxe4 5.Nxe4 d5 6.Bd3 dxe4 7.Bxe4 White has a comfortable position.

{edit: 7...Ne7 8.c3 is nothing White has to worry about]

Try 4. d3, which activates the Queen's Bishop. You may want to play a3 as well to retreat the King's Bishop after ...Na5 (but if 4...Na5, 5.Nxe5 should win).

In the main line there is 4...Nxe4 5.O-O but it's not that great. Sometimes I get 5.Bxe4 Qxe4 6.Nc3 Qd8 (I don't feel comfy with the queen in other places.) 7.d3 Bg4 when the pin is annoying.

Do you honestly think White has an advantage?

No lol.

Not bad, but not best.

Yep.  Black should try 4..Nxe4  for example 5.Bxf7+ Kxf7 6.Nxe4 turns out that Black's King is reasonably safe and he gets time to consolidate with good chances.

For your level, if an opponent cannot get you chekmated or material advantage in 10 moves, I think it is ok. At his level, he can think it is a bad position, but he should play the position vs a player with the same level, and not you. 

Because whatever opening or moves you make at your level, I am certain he can find a better refutation. Because you say he is good.

If he is your mentor, then you should listen to him atm. But he should take your level into consideration.

As Black, I would play 4. ... Bb4 followed by 0-0 sometime later to protect  f7 pawn. Or I can play 4. ... h3. But don't count on me, because I seldom to never play 1. .... e5.