In this post I will explain how Spellstrike grants a Magus an extra attack, with references, and also touch on why GMs do--and should not--rule against this in official play.
For the purposes of this explanation I will be referring to the default Magus only, with no archetypes or multiclassing.
1. WHAT DOES A MAGUS DO?
A Magus is designed to do one thing only: deal a lot of damage in combat with a combination of weapons and magic. They (a) do not have the HP or AC to handle front-line combat without magic, (b) do not have the breadth of magical utility one would have with a full caster, (c) do not have enough class skills or skill ranks to be a reliable skill monkey, and (d) do not have the Charisma to be the party face.
While the Magus can be quite powerful, it's not the best at anything it does and is mainly used by players who enjoy the fluff or have a specific concept in mind.
2. SPELL COMBAT
The first of the class features that define the Magus is Spell Combat. Spell Combat allows a Magus to wield a weapon in one hand while casting spells with the other. This operates as Two-Weapon Fighting, including the penalties to attack. In other words, where another character with TWF would get a main hand attack and an off hand attack, the Magus gets a main hand attack and an off hand spell. Please note that this means a 1st Level Magus can make two "attacks" per round as long as the second "attack" is a spell.
3. SPELLSTRIKE
Spellstrike is not an ability. It is not an action. It is not an attack. It doesn't cost anything to use. It is a class feature, which means it is "always on". And, most importantly, it does not affect Spell Combat in any way. A Magus can use Spellstrike and Spell Combat together or independently however they please.
To paraphrase Spellstrike... the Magus can choose to deliver a touch spell through any weapon they are wielding as part of a free melee attack.
When you choose to combine that with Spell Combat, you can make a normal melee attack, cast a touch spell, and then attack with your weapon a second time, dealing both weapon damage and spell damage. In addition, the spell has the chance to deal critical damage according to the weapon's critical range.
This is where the hangup is. Some GMs believe that you don't get that extra attack. Instead, they believe that Spellstrike only gives you the option to apply the spell damage to your first attack.
4. BUT WHY?
Well, put simply, that's a lot of potential burst damage for a 2nd Level character. Enough to one-shot certain bosses. At first glance this appears broken, so even though the Rules As Written (RAW) clearly state that you get an extra attack, the GM may claim that the wording is vague and your damage output should be lower per Rules As Intended (RAI).
In a home game, a GM is fully within their rights to nerf a class for any reason if they don't like it, but official games are a different beast. Your character is meant to play the same way regardless of which table you're playing at, and that doesn't work if GMs are second-guessing RAW. We want a consistent experience, and we also don't want players getting conflicting information from multiple GMs.
So here's why the GMs who say you don't get that extra attack are wrong.
5a. TWO WEAPON FIGHTING
You get two "attacks", even if one of them is technically a spell. When using normal TWF, you don't deal your off hand damage as part of your main hand attack. You roll for it separately. Since your touch spell is, for all intents and purposes, your off hand attack, you roll for it separately. Your main hand attack should in no way influence or be influenced by your off hand.
5b. MELEE TOUCH ATTACKS
Melee touch attacks from spells all function the same way, regardless of which class is casting them. First, you cast the spell (we'll say it's Shocking Grasp). Your hand is now wreathed in electricity. Second, you reach out and touch an enemy. This is your attack roll against your target's Touch AC, and it is defined in the rules as a free melee touch attack. If you succeed, they get zapped. If you fail, your hand is still wreathed in electricity and you get to try again on your next turn, unless you choose to dispel it. This is how melee touch spells are balanced against spells that don't require an attack roll to deal damage.
Spellstrike allows the Magus to substitute that free melee touch attack with a free melee attack using their weapon, rolling against your target's normal AC instead of their Touch AC, and dealing weapon damage in addition to the spell's effects if it hits.
5c. FREE ATTACKS
"Free attack" is a term that is well defined in the rules. For example, an Attack of Opportunity is a type of free attack. It means exactly what it says: you get a free attack regardless of what actions you took on your turn. Many abilities put limitations on how many free attacks you can have (you only get one attack of opportunity per round by default). Spellstrike does not. If you are casting a melee touch spell, you get a free attack.
6. WHY YOUR GM SHOULD ACCEPT THIS
Simply put, it's not broken at all. It's all burst damage. Your standard 2nd Level Magus can only do this once, maybe twice per day unless they use all of their spell slots for Shocking Grasp. After they've used them up, they're stuck in melee combat with a d8 hit die, light armor, no shield, only one weapon, and an attack bonus that's roughly half of a well-built Fighter's.
Magus damage progression also slows down somewhat rapidly. At 5th Level, that well-built Fighter gets two attacks with at least eight bonus damage each and a decent chance to hit with them, while the Magus still only gets their regular attack and one free attack from Spellstrike.
That burst damage is the only real advantage a Magus gets at low levels. Knee-jerk reactions to that damage only serve to halt combat for an extended period while the rules get referenced and argued, and may also result in character death.
Not to mention, Jason Bulmahn himself has stated it's an extra attack, and is designed to be a bonus. While he made this statement during the Magus' testing phase, said statement was never altered, redacted, or expanded and can therefore be considered the official response. (Jason Bulmahn's Post)
In conclusion, be excellent to each other, and if you absolutely must call any of this into question, please wait until the session is over. Your Magus came prepared to play Pathfinder, not defend their thesis.
Thank you.