Here's what I think is the real reason behind the attack on Konoha by a 15-16 year old Obito.

Objectives :

Primary Objective - The elimination of Kushina Uzumaki.
Secondary Objectives - Unleash Kurama on the leaf.

Reasons :

1. Rin's death :

Obito who Loved Rin almost all his life and saw her death by his very own eye. Now we know that he entrusted his Sharingan to Kakashi in order to protect Rin and we know what happened -

2. Minato's Lack of Responsibility :

Though Zetsu said that Minato was busy with other Mission Obito is visibly pissed on his Sensei :

3. Why Blame it on Minato?? :

Remember how Tobi had detailed knowledge on Minato's FTG [He was fooled by FTG Level 2]. I believe he thought that Minato had S/T so he could've saved Rin [After all he saw Minato giving his FTG Kunai to Kakashi] so it plausible that he made that assumption that Minato could've saved her if he wanted to but he didn't.

Here we see Tobi talking about FTG -

the same tech that had failed to save his Rin so he would've liked nothing better than Killing Kushina and FTG failing in saving her and yes the Minato failed to make it in time.

The Plan and its execution :

Here we see that Obito succeeded in completing the Primary Objective of his Plan. He knew that extraction of bijju means death -

He Immediately went into the Leaf Village and summoned Kurama. And Kurama started doing his thing i.e. Destroying everything. But before that He saw Minato coming and taking Kushina away -

Focus on how he says Gone Again, No Matter. Now if his primary objective was to destroys Konoha he'd have followed Minato and made sure that he gets eliminated first but it didn't matter because his Mission was almost complete!

We know that Minato then came and sent a TBB away but Obito couldn't fight the urge to have a go at his sensei, I mean he came for Kushina and that's what the trigger was and that's why he attacked Minato.

Here we can see he wants to end Minato and that's why the Avenger-Obito speaks YOU will face ME!

We know how that Fight went. What I believe that 15 year old Obito with a Zetsu shell and newly acquired Kamui knew that he couldn't beat his Sensei and that's why his mission avoided fighting Minato [Plus there was a chance of Minato finding about his Identity as well] but the events that happened in the execution process triggered the fight.

In that fight Minato asked him whether he was Madara and that's when Obito spoke of Madara's Ideology -

After the fight Obito left with bold statements and no regrets [his mission was a success] but he also said that Minato deserves the title of the 4th Hokage.

Theory about Obito's S/T Ninjutsu :

WE know that Obito can use the S/T via his Kamui [or his Kamui is his s/t ninjutsu] but its said that for S/T ninjutsu you need Marking and Obito seems to pull it off without it.

Kakashi even said that His s/t surpasses Minato's. Heck Minato said that Obito's S/T surpasses his own as well as Tobirama's -

But the answer is -

This bastard is all over the place -

In short Zetsu has an underground Network [Like a Subway ] and that's why Obito can go to anywhere if there's a zetsu checkpoint. And that's why he doesn't necessarily need the Marking or Seals to teleport and that's why his S/T is superior to Minato's and Tobirama's.

Summary :

1. Obito's main objective was to kill Kushina and Secondary was to unleash Kurama on the leaf.
2. His objective also included avoiding direct fight with Minato [fear of being recognized] but the course of events that happened he attacked Minato.
3. Obito succeeded in his Mission even though he lost the fight to Minato or the control over Kurama.
4. Obito's S/T [Kamui] uses the Zetsu's underground network instead of Marking or Seals and that's why wherever zetsu has his underground clones he can appear their [w/out markings]

For those who hate to read long Paras You can read "Objectives" and the "Summary"